Master File
Joanna Duran, Nikhil Gupta, Max Moro
2019-03-28 22:21:03
User Inputs
output.var = params$output.var
transform.abs = FALSE
log.pred = params$log.pred
norm.pred = params$norm.pred
eda = params$eda
algo.forward.caret = params$algo.forward.caret
algo.backward.caret = params$algo.backward.caret
algo.stepwise.caret = params$algo.stepwise.caret
algo.LASSO.caret = params$algo.LASSO.caret
algo.LARS.caret = params$algo.LARS.caret
message("Parameters used for training/prediction: ")## Parameters used for training/prediction:str(params)## List of 9
## $ output.var : chr "y3"
## $ log.pred : logi TRUE
## $ norm.pred : logi FALSE
## $ eda : logi FALSE
## $ algo.forward.caret : logi TRUE
## $ algo.backward.caret: logi TRUE
## $ algo.stepwise.caret: logi TRUE
## $ algo.LASSO.caret : logi TRUE
## $ algo.LARS.caret : logi TRUE# Setup Labels
output.var.tr = if (log.pred == TRUE) paste0(output.var,'.log') else output.var.tr = output.var
# output.var.tr = if (log.pred == TRUE) paste0(output.var,'.cuberoot') else output.var.tr = output.var
# output.var.tr = if (norm.pred == TRUE) paste0(output.var,'.bestnorm') else output.var.tr = output.varLoading Data
feat = read.csv('../../Data/features_highprec.csv')
labels = read.csv('../../Data/labels.csv')
predictors = names(dplyr::select(feat,-JobName))
data.ori = inner_join(feat,labels,by='JobName')
#data.ori = inner_join(feat,select_at(labels,c('JobName',output.var)),by='JobName')Data validation
cc = complete.cases(data.ori)
data.notComplete = data.ori[! cc,]
data = data.ori[cc,] %>% select_at(c(predictors,output.var,'JobName'))
message('Original cases: ',nrow(data.ori))## Original cases: 10000message('Non-Complete cases: ',nrow(data.notComplete))## Non-Complete cases: 3020message('Complete cases: ',nrow(data))## Complete cases: 6980summary(dplyr::select_at(data,c('JobName',output.var)))## JobName y3
## Job_00001: 1 Min. : 95.91
## Job_00002: 1 1st Qu.:118.29
## Job_00003: 1 Median :124.03
## Job_00004: 1 Mean :125.40
## Job_00007: 1 3rd Qu.:131.06
## Job_00008: 1 Max. :193.73
## (Other) :6974Output Variable
The Output Variable y3 shows right skewness, so will proceed with a log transformation
Histogram
df=gather(select_at(data,output.var))
ggplot(df, aes(x=value)) +
geom_histogram(aes(y=..density..),bins = 50,fill='light blue') +
geom_density() 
#stat_function(fun = dnorm, n = 100, args = list(mean = mean(df$value), sd = sd(df$value))) QQPlot
ggplot(gather(select_at(data,output.var)), aes(sample=value)) +
stat_qq() +
facet_wrap(~key, scales = 'free',ncol=4)
Trasformation of Output Variable from y3 to y3.log
if(log.pred==TRUE) data[[output.var.tr]] = log(data[[output.var]],10) else
# if(log.pred==TRUE) data[[output.var.tr]] = (data[[output.var]])^(1/3) else
data[[output.var.tr]] = data[[output.var]]
df=gather(select_at(data,c(output.var,output.var.tr)))
ggplot(df, aes(value)) +
geom_histogram(aes(y=..density..),bins = 50,fill='light blue') +
geom_density() +
# stat_function(fun = dnorm, n = 100, args = list(mean = mean(df$value), sd = sd(df$value)))
facet_wrap(~key, scales = 'free',ncol=2)
ggplot(gather(select_at(data,c(output.var,output.var.tr))), aes(sample=value)) +
stat_qq() +
facet_wrap(~key, scales = 'free',ncol=4)
Best Normalizator y3
Normalization of y3 using bestNormalize package. (suggested orderNorm) This is cool, but I think is too far for the objective of the project
if (norm.pred == TRUE){
t=bestNormalize::bestNormalize(data[[output.var]])
t
qqnorm(data[[output.var]])
qqnorm(predict(t))
data[[output.var.tr]] = predict(t)
}orderNorm() is a rank-based procedure by which the values of a vector are mapped to their percentile, which is then mapped to the same percentile of the normal distribution. Without the presence of ties, this essentially guarantees that the transformation leads to a uniform distribution
Predictors
Feature Engineering
data$x2byx1 = data$x2/data$x1
data$x6byx5 = data$x6/data$x5
data$x9byx7 = data$x9/data$x7
data$x10byx8 = data$x10/data$x8
data$x14byx12 = data$x14/data$x12
data$x15byx13 = data$x15/data$x13
data$x17byx16 = data$x17/data$x16
data$x19byx18 = data$x19/data$x18
data$x21byx20 = data$x21/data$x20
data$x23byx22 = data$x23/data$x22
data$x1log = log(data$x1)
data$x2log = log(data$x2)
data$x5log = log(data$x5)
data$x6log = log(data$x6)
data$x7log = log(data$x7)
data$x9log = log(data$x9)
data$x8log = log(data$x8)
data$x10log = log(data$x10)
data$x12log = log(data$x12)
data$x14log = log(data$x14)
data$x13log = log(data$x13)
data$x15log = log(data$x15)
data$x16log = log(data$x16)
data$x17log = log(data$x17)
data$x18log = log(data$x18)
data$x19log = log(data$x19)
data$x20log = log(data$x20)
data$x21log = log(data$x21)
data$x22log = log(data$x22)
data$x23log = log(data$x23)data$x11log = log(data$x11)data$x1sqinv = 1/(data$x1)^2
data$x5sqinv = 1/(data$x5)^2
data$x7sqinv = 1/(data$x7)^2
data$x8sqinv = 1/(data$x8)^2
data$x12sqinv = 1/(data$x12)^2
data$x13sqinv = 1/(data$x13)^2
data$x16sqinv = 1/(data$x16)^2
data$x18sqinv = 1/(data$x18)^2
data$x20sqinv = 1/(data$x20)^2
data$x22sqinv = 1/(data$x22)^2 predictors## [1] "x1" "x2" "x3" "x4" "x5" "x6" "x7" "x8" "x9" "x10" "x11"
## [12] "x12" "x13" "x14" "x15" "x16" "x17" "x18" "x19" "x20" "x21" "x22"
## [23] "x23" "stat1" "stat2" "stat3" "stat4" "stat5" "stat6" "stat7" "stat8" "stat9" "stat10"
## [34] "stat11" "stat12" "stat13" "stat14" "stat15" "stat16" "stat17" "stat18" "stat19" "stat20" "stat21"
## [45] "stat22" "stat23" "stat24" "stat25" "stat26" "stat27" "stat28" "stat29" "stat30" "stat31" "stat32"
## [56] "stat33" "stat34" "stat35" "stat36" "stat37" "stat38" "stat39" "stat40" "stat41" "stat42" "stat43"
## [67] "stat44" "stat45" "stat46" "stat47" "stat48" "stat49" "stat50" "stat51" "stat52" "stat53" "stat54"
## [78] "stat55" "stat56" "stat57" "stat58" "stat59" "stat60" "stat61" "stat62" "stat63" "stat64" "stat65"
## [89] "stat66" "stat67" "stat68" "stat69" "stat70" "stat71" "stat72" "stat73" "stat74" "stat75" "stat76"
## [100] "stat77" "stat78" "stat79" "stat80" "stat81" "stat82" "stat83" "stat84" "stat85" "stat86" "stat87"
## [111] "stat88" "stat89" "stat90" "stat91" "stat92" "stat93" "stat94" "stat95" "stat96" "stat97" "stat98"
## [122] "stat99" "stat100" "stat101" "stat102" "stat103" "stat104" "stat105" "stat106" "stat107" "stat108" "stat109"
## [133] "stat110" "stat111" "stat112" "stat113" "stat114" "stat115" "stat116" "stat117" "stat118" "stat119" "stat120"
## [144] "stat121" "stat122" "stat123" "stat124" "stat125" "stat126" "stat127" "stat128" "stat129" "stat130" "stat131"
## [155] "stat132" "stat133" "stat134" "stat135" "stat136" "stat137" "stat138" "stat139" "stat140" "stat141" "stat142"
## [166] "stat143" "stat144" "stat145" "stat146" "stat147" "stat148" "stat149" "stat150" "stat151" "stat152" "stat153"
## [177] "stat154" "stat155" "stat156" "stat157" "stat158" "stat159" "stat160" "stat161" "stat162" "stat163" "stat164"
## [188] "stat165" "stat166" "stat167" "stat168" "stat169" "stat170" "stat171" "stat172" "stat173" "stat174" "stat175"
## [199] "stat176" "stat177" "stat178" "stat179" "stat180" "stat181" "stat182" "stat183" "stat184" "stat185" "stat186"
## [210] "stat187" "stat188" "stat189" "stat190" "stat191" "stat192" "stat193" "stat194" "stat195" "stat196" "stat197"
## [221] "stat198" "stat199" "stat200" "stat201" "stat202" "stat203" "stat204" "stat205" "stat206" "stat207" "stat208"
## [232] "stat209" "stat210" "stat211" "stat212" "stat213" "stat214" "stat215" "stat216" "stat217"controlled.vars = colnames(data)[grep("^x",colnames(data))]
stat.vars = colnames(data)[grep("^stat",colnames(data))]
predictors = c(controlled.vars,stat.vars)
predictors## [1] "x1" "x2" "x3" "x4" "x5" "x6" "x7" "x8" "x9" "x10"
## [11] "x11" "x12" "x13" "x14" "x15" "x16" "x17" "x18" "x19" "x20"
## [21] "x21" "x22" "x23" "x2byx1" "x6byx5" "x9byx7" "x10byx8" "x14byx12" "x15byx13" "x17byx16"
## [31] "x19byx18" "x21byx20" "x23byx22" "x1log" "x2log" "x5log" "x6log" "x7log" "x9log" "x8log"
## [41] "x10log" "x12log" "x14log" "x13log" "x15log" "x16log" "x17log" "x18log" "x19log" "x20log"
## [51] "x21log" "x22log" "x23log" "x11log" "x1sqinv" "x5sqinv" "x7sqinv" "x8sqinv" "x12sqinv" "x13sqinv"
## [61] "x16sqinv" "x18sqinv" "x20sqinv" "x22sqinv" "stat1" "stat2" "stat3" "stat4" "stat5" "stat6"
## [71] "stat7" "stat8" "stat9" "stat10" "stat11" "stat12" "stat13" "stat14" "stat15" "stat16"
## [81] "stat17" "stat18" "stat19" "stat20" "stat21" "stat22" "stat23" "stat24" "stat25" "stat26"
## [91] "stat27" "stat28" "stat29" "stat30" "stat31" "stat32" "stat33" "stat34" "stat35" "stat36"
## [101] "stat37" "stat38" "stat39" "stat40" "stat41" "stat42" "stat43" "stat44" "stat45" "stat46"
## [111] "stat47" "stat48" "stat49" "stat50" "stat51" "stat52" "stat53" "stat54" "stat55" "stat56"
## [121] "stat57" "stat58" "stat59" "stat60" "stat61" "stat62" "stat63" "stat64" "stat65" "stat66"
## [131] "stat67" "stat68" "stat69" "stat70" "stat71" "stat72" "stat73" "stat74" "stat75" "stat76"
## [141] "stat77" "stat78" "stat79" "stat80" "stat81" "stat82" "stat83" "stat84" "stat85" "stat86"
## [151] "stat87" "stat88" "stat89" "stat90" "stat91" "stat92" "stat93" "stat94" "stat95" "stat96"
## [161] "stat97" "stat98" "stat99" "stat100" "stat101" "stat102" "stat103" "stat104" "stat105" "stat106"
## [171] "stat107" "stat108" "stat109" "stat110" "stat111" "stat112" "stat113" "stat114" "stat115" "stat116"
## [181] "stat117" "stat118" "stat119" "stat120" "stat121" "stat122" "stat123" "stat124" "stat125" "stat126"
## [191] "stat127" "stat128" "stat129" "stat130" "stat131" "stat132" "stat133" "stat134" "stat135" "stat136"
## [201] "stat137" "stat138" "stat139" "stat140" "stat141" "stat142" "stat143" "stat144" "stat145" "stat146"
## [211] "stat147" "stat148" "stat149" "stat150" "stat151" "stat152" "stat153" "stat154" "stat155" "stat156"
## [221] "stat157" "stat158" "stat159" "stat160" "stat161" "stat162" "stat163" "stat164" "stat165" "stat166"
## [231] "stat167" "stat168" "stat169" "stat170" "stat171" "stat172" "stat173" "stat174" "stat175" "stat176"
## [241] "stat177" "stat178" "stat179" "stat180" "stat181" "stat182" "stat183" "stat184" "stat185" "stat186"
## [251] "stat187" "stat188" "stat189" "stat190" "stat191" "stat192" "stat193" "stat194" "stat195" "stat196"
## [261] "stat197" "stat198" "stat199" "stat200" "stat201" "stat202" "stat203" "stat204" "stat205" "stat206"
## [271] "stat207" "stat208" "stat209" "stat210" "stat211" "stat212" "stat213" "stat214" "stat215" "stat216"
## [281] "stat217"All predictors show a Fat-Tail situation, where the two tails are very tall, and a low distribution around the mean. The orderNorm transformation can help (see [Best Normalizator] section)
Interesting Predictors
Histograms
if (eda == TRUE){
cols = c('x11','x18','stat98','x7','stat110')
df=gather(select_at(data,cols))
ggplot(df, aes(value)) +
geom_histogram(aes(y=..density..),bins = 50,fill='light blue') +
geom_density() +
# stat_function(fun = dnorm, n = 100, args = list(mean = mean(df$value), sd = sd(df$value)))
facet_wrap(~key, scales = 'free',ncol=3)
# ggplot(gather(select_at(data,cols)), aes(sample=value)) +
# stat_qq()+
# facet_wrap(~key, scales = 'free',ncol=2)
lapply(select_at(data,cols),summary)
}Scatter plot vs. output variable **y3.log
if (eda == TRUE){
d = gather(dplyr::select_at(data,c(cols,output.var.tr)),key=target,value=value,-!!output.var.tr)
ggplot(data=d, aes_string(x='value',y=output.var.tr)) +
geom_point(color='light green',alpha=0.5) +
geom_smooth() +
facet_wrap(~target, scales = 'free',ncol=3)
}All Predictors
Histograms
All indicators have a strong indication of Fat-Tails
if (eda == TRUE){
df=gather(select_at(data,predictors))
ggplot(df, aes(value)) +
geom_histogram(aes(y=..density..),bins = 50,fill='light blue') +
geom_density() +
# stat_function(fun = dnorm, n = 100, args = list(mean = mean(df$value), sd = sd(df$value)))
facet_wrap(~key, scales = 'free',ncol=4)
}Correlations
With Output Variable
if (eda == TRUE){
#chart.Correlation(select(data,-JobName), pch=21)
# https://stackoverflow.com/questions/27034655/how-to-use-dplyrarrangedesc-when-using-a-string-as-column-name
t=as.data.frame(round(cor(dplyr::select(data,-one_of(output.var.tr,'JobName'))
,select_at(data,output.var.tr)),4)) %>%
#rownames_to_column(var='variable') %>% filter(variable != !!output.var) %>% arrange(-y3.log)
rownames_to_column(var='variable') %>% filter(variable != !!output.var) %>% arrange(-!!sym(output.var.tr))
#DT::datatable(t)
message("Top Positive")
#kable(head(arrange(t,desc(y3.log)),20))
kable(head(arrange(t,desc(!!sym(output.var.tr))),20))
message("Top Negative")
#kable(head(arrange(t,y3.log),20))
kable(head(arrange(t,!!sym(output.var.tr)),20))
}Between All Variables
if (eda == TRUE){
#chart.Correlation(select(data,-JobName), pch=21)
t=as.data.frame(round(cor(dplyr::select(data,-one_of('JobName'))),4))
#DT::datatable(t,options=list(scrollX=T))
message("Showing only 10 variables")
kable(t[1:10,1:10])
}Scatter Plots with Output Variable
Scatter plots with all predictors and the output variable (y3.log)
if (eda == TRUE){
d = gather(dplyr::select_at(data,c(predictors,output.var.tr)),key=target,value=value,-!!output.var.tr)
ggplot(data=d, aes_string(x='value',y=output.var.tr)) +
geom_point(color='light blue',alpha=0.5) +
geom_smooth() +
facet_wrap(~target, scales = 'free',ncol=4)
}Multicollinearity - VIF
No Multicollinearity among predictors
Showing Top predictor by VIF Value
if (eda == TRUE){
vifDF = usdm::vif(select_at(data,predictors)) %>% arrange(desc(VIF))
head(vifDF,75)
}Feature Eng
- Square Root transformation for x18
data.tr=data %>%
mutate(x18.sqrt = sqrt(x18))
cols=c('x18','x18.sqrt')Comparing Pre and Post Transformation Density Plots
# ggplot(gather(select_at(data.tr,cols)), aes(value)) +
# geom_histogram(aes(y=..density..),bins = 50,fill='light blue') +
# geom_density() +
# facet_wrap(~key, scales = 'free',ncol=4)
d = gather(dplyr::select_at(data.tr,c(cols,output.var.tr)),key=target,value=value,-!!output.var.tr)
ggplot(data=d, aes_string(x='value',y=output.var.tr)) +
geom_point(color='light blue',alpha=0.5) +
geom_smooth() +
facet_wrap(~target, scales = 'free',ncol=4)## `geom_smooth()` using method = 'gam' and formula 'y ~ s(x, bs = "cs")'
#removing unwanted variables
data.tr=data.tr %>%
#dplyr::select_at(names(data.tr)[! names(data.tr) %in% c('x18','y3','JobName')])
dplyr::select_at(names(data.tr)[! names(data.tr) %in% c('JobName')])
data=data.tr
label.names=output.var.trModeling
PCA
# 0 for no interaction,
# 1 for Full 2 way interaction and
# 2 for Selective 2 way interaction
# 3 for Selective 3 way interaction
InteractionMode = 2
pca.vars = names(data)
pca.vars = pca.vars[!pca.vars %in% label.names]
# http://sshaikh.org/2015/05/06/parallelize-machine-learning-in-r-with-multi-core-cpus/
# #cl <- makeCluster(ceiling(detectCores()*0.5)) # use 75% of cores only, leave rest for other tasks
cl <- makeCluster(detectCores()*0.75) # use 75% of cores only, leave rest for other tasks
registerDoParallel(cl)
if(InteractionMode == 1){
pca.formula =as.formula(paste0('~(',paste0(pca.vars, collapse ='+'),')^2'))
pca.model = prcomp(formula=pca.formula,data=data[,pca.vars],center=T,scale.=T,retx = T)
#saveRDS(pca.model,'pca.model.rds')
}
if (InteractionMode == 0){
pca.model = prcomp(x=data[,pca.vars],center=T,scale.=T,retx = T)
}
if (InteractionMode >= 2 & InteractionMode <= 3){
controlled.vars = pca.vars[grep("^x",pca.vars)]
stat.vars = pca.vars[grep("^stat",pca.vars)]
if (InteractionMode >= 2){
interaction.form = paste0('~(',paste0(controlled.vars, collapse ='+'),')^2')
}
if (InteractionMode >= 3){
interaction.form = paste0('~(',paste0(controlled.vars, collapse ='+'),')^3')
}
no.interact.form = paste0(stat.vars, collapse ='+')
pca.formula = as.formula(paste(interaction.form, no.interact.form, sep = "+"))
pca.model = prcomp(formula=pca.formula,data=data[,pca.vars],center=T,scale.=T,retx = T)
}
stopCluster(cl)
registerDoSEQ() # register sequential engine in case you are not using this function anymoretargetCumVar = .9
pca.model$var = pca.model$sdev ^ 2 #eigenvalues
pca.model$pvar = pca.model$var / sum(pca.model$var)
pca.model$cumpvar = cumsum(pca.model$pvar )
pca.model$pcaSel = pca.model$cumpvar<=targetCumVar
pca.model$pcaSelCount = sum(pca.model$pcaSel)
pca.model$pcaSelTotVar = sum(pca.model$pvar[pca.model$pcaSel])
message(pca.model$pcaSelCount, " PCAs justify ",percent(targetCumVar)," of the total Variance. (",percent(pca.model$pcaSelTotVar),")")## 164 PCAs justify 90.0% of the total Variance. (90.0%)plot(pca.model$var,xlab="Principal component", ylab="Proportion of variance explained", type='b')
plot(cumsum(pca.model$pvar ),xlab="Principal component", ylab="Cumulative Proportion of variance explained", ylim=c(0,1), type='b')
screeplot(pca.model,npcs = pca.model$pcaSelCount)
screeplot(pca.model,npcs = pca.model$pcaSelCount,type='lines')
#summary(pca.model)
#pca.model$rotation
#creating dataset
data.pca = dplyr::select(data,!!label.names) %>%
dplyr::bind_cols(dplyr::select(as.data.frame(pca.model$x)
,!!colnames(pca.model$rotation)[pca.model$pcaSel])
)Train Test Split
data.pca = data.pca[sample(nrow(data.pca)),] # randomly shuffle data
split = sample.split(data.pca[,label.names], SplitRatio = 0.8)
data.train = subset(data.pca, split == TRUE)
data.test = subset(data.pca, split == FALSE)Common Functions
plot.diagnostics <- function(model, train) {
plot(model)
residuals = resid(model) # Plotted above in plot(lm.out)
r.standard = rstandard(model)
r.student = rstudent(model)
df = data.frame(x=predict(model,train),y=r.student)
p=ggplot(data=df,aes(x=x,y=y)) +
geom_point(color='blue',alpha=0.5,shape=20,size=2) +
geom_hline(yintercept = 0,size=1)+
ylab("Student Residuals") +
xlab("Predicted Values")+
ggtitle("Student Residual Plot")
plot(p)
df = data.frame(x=predict(model,train),y=r.standard)
p=ggplot(data=df,aes(x=x,y=y)) +
geom_point(color='blue',alpha=0.5,shape=20,size=2) +
geom_hline(yintercept = c(-2,0,2),size=1)+
ylab("Student Residuals") +
xlab("Predicted Values")+
ggtitle("Student Residual Plot")
plot(p)
# Histogram
df=data.frame(r.student)
p=ggplot(data=df,aes(r.student)) +
geom_histogram(aes(y=..density..),bins = 50,fill='blue',alpha=0.6) +
stat_function(fun = dnorm, n = 100, args = list(mean = 0, sd = 1)) +
ylab("Density")+
xlab("Studentized Residuals")+
ggtitle("Distribution of Studentized Residuals")
plot(p)
# http://www.stat.columbia.edu/~martin/W2024/R7.pdf
# Influential plots
inf.meas = influence.measures(model)
# print (summary(inf.meas)) # too much data
# Leverage plot
lev = hat(model.matrix(model))
df=tibble::rownames_to_column(as.data.frame(lev),'id')
p=ggplot(data=df,aes(x=as.numeric(id),y=lev)) +
geom_point(color='blue',alpha=0.5,shape=20,size=2) +
ylab('Leverage - check') +
xlab('Index')
plot(p)
# Cook's Distance
cd = cooks.distance(model)
df=tibble::rownames_to_column(as.data.frame(cd),'id')
p=ggplot(data=df,aes(x=as.numeric(id),y=cd)) +
geom_point(color='blue',alpha=0.5,shape=20,size=2) +
geom_text(data=filter(df,cd>15/nrow(train)),aes(label=id),check_overlap=T,size=3,vjust=-.5)+
ylab('Cooks distances') +
geom_hline(yintercept = c(4/nrow(train),0),size=1)+
xlab('Index')
plot(p)
print (paste("Number of data points that have Cook's D > 4/n: ", length(cd[cd > 4/nrow(train)]), sep = ""))
print (paste("Number of data points that have Cook's D > 1: ", length(cd[cd > 1]), sep = ""))
return(cd)
}
# function to set up random seeds
# Based on http://jaehyeon-kim.github.io/2015/05/Setup-Random-Seeds-on-Caret-Package.html
setCaretSeeds <- function(method = "cv", numbers = 1, repeats = 1, tunes = NULL, seed = 1701) {
#B is the number of resamples and integer vector of M (numbers + tune length if any)
B <- if (method == "cv") numbers
else if(method == "repeatedcv") numbers * repeats
else NULL
if(is.null(length)) {
seeds <- NULL
} else {
set.seed(seed = seed)
seeds <- vector(mode = "list", length = B)
seeds <- lapply(seeds, function(x) sample.int(n = 1000000
, size = numbers + ifelse(is.null(tunes), 0, tunes)))
seeds[[length(seeds) + 1]] <- sample.int(n = 1000000, size = 1)
}
# return seeds
seeds
}
train.caret.glmselect = function(formula, data, method
,subopt = NULL, feature.names
, train.control = NULL, tune.grid = NULL, pre.proc = NULL){
if(is.null(train.control)){
train.control <- trainControl(method = "cv"
,number = 10
,seeds = setCaretSeeds(method = "cv"
, numbers = 10
, seed = 1701)
,search = "grid"
,verboseIter = TRUE
,allowParallel = TRUE
)
}
if(is.null(tune.grid)){
if (method == 'leapForward' | method == 'leapBackward' | method == 'leapSeq'){
tune.grid = data.frame(nvmax = 1:length(feature.names))
}
if (method == 'glmnet' && subopt == 'LASSO'){
# Will only show 1 Lambda value during training, but that is OK
# https://stackoverflow.com/questions/47526544/why-need-to-tune-lambda-with-carettrain-method-glmnet-and-cv-glmnet
# Another option for LASSO is this: https://github.com/topepo/caret/blob/master/RegressionTests/Code/lasso.R
lambda = 10^seq(-2,0, length =100)
alpha = c(1)
tune.grid = expand.grid(alpha = alpha,lambda = lambda)
}
if (method == 'lars'){
# https://github.com/topepo/caret/blob/master/RegressionTests/Code/lars.R
fraction = seq(0, 1, length = 100)
tune.grid = expand.grid(fraction = fraction)
pre.proc = c("center", "scale")
}
}
# http://sshaikh.org/2015/05/06/parallelize-machine-learning-in-r-with-multi-core-cpus/
# #cl <- makeCluster(ceiling(detectCores()*0.5)) # use 75% of cores only, leave rest for other tasks
cl <- makeCluster(detectCores()*0.75) # use 75% of cores only, leave rest for other tasks
registerDoParallel(cl)
set.seed(1)
# note that the seed has to actually be set just before this function is called
# settign is above just not ensure reproducibility for some reason
model.caret <- caret::train(formula
, data = data
, method = method
, tuneGrid = tune.grid
, trControl = train.control
, preProc = pre.proc
)
stopCluster(cl)
registerDoSEQ() # register sequential engine in case you are not using this function anymore
if (method == 'leapForward' | method == 'leapBackward' | method == 'leapSeq'){
print("All models results")
print(model.caret$results) # all model results
print("Best Model")
print(model.caret$bestTune) # best model
model = model.caret$finalModel
# Metrics Plot
dataPlot = model.caret$results %>%
gather(key='metric',value='value',-nvmax) %>%
dplyr::filter(metric %in% c('MAE','RMSE','Rsquared'))
metricsPlot = ggplot(data=dataPlot,aes(x=nvmax,y=value) ) +
geom_line(color='lightblue4') +
geom_point(color='blue',alpha=0.7,size=.9) +
facet_wrap(~metric,ncol=2,scales='free_y')+
theme_light()
plot(metricsPlot)
# Residuals Plot
# leap function does not support studentized residuals
dataPlot=data.frame(pred=predict(model.caret,data),res=resid(model.caret))
residPlot = ggplot(dataPlot,aes(x=pred,y=res)) +
geom_point(color='light blue',alpha=0.7) +
geom_smooth(method="lm")+
theme_light()
plot(residPlot)
residHistogram = ggplot(dataPlot,aes(x=res)) +
geom_histogram(aes(y=..density..),fill='light blue',alpha=1) +
#geom_density(color='lightblue4') +
stat_function(fun = dnorm, n = 100, args = list(mean = mean(dataPlot$res)
, sd = sd(dataPlot$res)),color='lightblue4')
theme_light()
plot(residHistogram)
id = rownames(model.caret$bestTune)
# Provides the coefficients of the best model
# regsubsets doens return a full model (see documentation of regsubset), so we need to recalcualte themodel
# https://stackoverflow.com/questions/13063762/how-to-obtain-a-lm-object-from-regsubsets
print("Coefficients of final model:")
coefs <- coef(model, id=id)
#calculate the model to the the coef intervals
nams <- names(coefs)
nams <- nams[!nams %in% "(Intercept)"]
response <- as.character(formula[[2]])
form <- as.formula(paste(response, paste(nams, collapse = " + "), sep = " ~ "))
mod <- lm(form, data = data)
#coefs
#coef(mod)
print(car::Confint(mod))
return(list(model = model,id = id, residPlot = residPlot, residHistogram=residHistogram
,modelLM=mod))
}
if (method == 'glmnet' && subopt == 'LASSO'){
print(model.caret)
print(plot(model.caret))
print(model.caret$bestTune)
print(model.caret$results)
model=model.caret$finalModel
# Metrics Plot
dataPlot = model.caret$results %>%
gather(key='metric',value='value',-lambda) %>%
dplyr::filter(metric %in% c('MAE','RMSE','Rsquared'))
metricsPlot = ggplot(data=dataPlot,aes(x=lambda,y=value) ) +
geom_line(color='lightblue4') +
geom_point(color='blue',alpha=0.7,size=.9) +
facet_wrap(~metric,ncol=2,scales='free_y')+
theme_light()
plot(metricsPlot)
# Residuals Plot
dataPlot=data.frame(pred=predict(model.caret,data),res=resid(model.caret))
residPlot = ggplot(dataPlot,aes(x=pred,y=res)) +
geom_point(color='light blue',alpha=0.7) +
geom_smooth(method="lm")+
theme_light()
plot(residPlot)
residHistogram = ggplot(dataPlot,aes(x=res)) +
geom_histogram(aes(y=..density..),fill='light blue',alpha=1) +
#geom_density(color='lightblue4') +
stat_function(fun = dnorm, n = 100, args = list(mean = mean(dataPlot$res)
, sd = sd(dataPlot$res)),color='lightblue4')
theme_light()
plot(residHistogram)
print("Coefficients")
#no interval for glmnet: https://stackoverflow.com/questions/39750965/confidence-intervals-for-ridge-regression
t=coef(model,s=model.caret$bestTune$lambda)
model.coef = t[which(t[,1]!=0),]
print(as.data.frame(model.coef))
id = NULL # not really needed but added for consistency
return(list(model = model.caret,id = id, residPlot = residPlot, metricsPlot=metricsPlot ))
}
if (method == 'lars'){
print(model.caret)
print(plot(model.caret))
print(model.caret$bestTune)
# Metrics Plot
dataPlot = model.caret$results %>%
gather(key='metric',value='value',-fraction) %>%
dplyr::filter(metric %in% c('MAE','RMSE','Rsquared'))
metricsPlot = ggplot(data=dataPlot,aes(x=fraction,y=value) ) +
geom_line(color='lightblue4') +
geom_point(color='blue',alpha=0.7,size=.9) +
facet_wrap(~metric,ncol=2,scales='free_y')+
theme_light()
plot(metricsPlot)
# Residuals Plot
dataPlot=data.frame(pred=predict(model.caret,data),res=resid(model.caret))
residPlot = ggplot(dataPlot,aes(x=pred,y=res)) +
geom_point(color='light blue',alpha=0.7) +
geom_smooth(method="lm")+
theme_light()
plot(residPlot)
residHistogram = ggplot(dataPlot,aes(x=res)) +
geom_histogram(aes(y=..density..),fill='light blue',alpha=1) +
#geom_density(color='lightblue4') +
stat_function(fun = dnorm, n = 100, args = list(mean = mean(dataPlot$res)
, sd = sd(dataPlot$res)),color='lightblue4')
theme_light()
plot(residHistogram)
print("Coefficients")
t=coef(model.caret$finalModel,s=model.caret$bestTune$fraction,mode='fraction')
model.coef = t[which(t!=0)]
print(model.coef)
id = NULL # not really needed but added for consistency
return(list(model = model.caret,id = id, residPlot = residPlot, residHistogram=residHistogram))
}
}
# https://stackoverflow.com/questions/48265743/linear-model-subset-selection-goodness-of-fit-with-k-fold-cross-validation
# changed slightly since call[[2]] was just returning "formula" without actually returnign the value in formula
predict.regsubsets <- function(object, newdata, id, formula, ...) {
#form <- as.formula(object$call[[2]])
mat <- model.matrix(formula, newdata) # adds intercept and expands any interaction terms
coefi <- coef(object, id = id)
xvars <- names(coefi)
return(mat[,xvars]%*%coefi)
}
test.model = function(model, test, level=0.95
,draw.limits = FALSE, good = 0.1, ok = 0.15
,method = NULL, subopt = NULL
,id = NULL, formula, feature.names, label.names
,transformation = NULL){
## if using caret for glm select equivalent functionality,
## need to pass formula (full is ok as it will select subset of variables from there)
if (is.null(method)){
pred = predict(model, newdata=test, interval="confidence", level = level)
}
if (method == 'leapForward' | method == 'leapBackward' | method == 'leapSeq'){
pred = predict.regsubsets(model, newdata = test, id = id, formula = formula)
}
if (method == 'glmnet' && subopt == 'LASSO'){
xtest = as.matrix(test[,feature.names])
pred=as.data.frame(predict(model, xtest))
}
if (method == 'lars'){
pred=as.data.frame(predict(model, newdata = test))
}
# Summary of predicted values
print ("Summary of predicted values: ")
print(summary(pred[,1]))
test.mse = mean((test[,label.names]-pred[,1])^2)
print (paste(method, subopt, "Test MSE:", test.mse, sep=" "))
test.rmse = sqrt(test.mse)
print (paste(method, subopt, "Test RMSE:", test.rmse, sep=" "))
if(log.pred == TRUE || norm.pred == TRUE){
# plot transformewd comparison first
df=data.frame(x=test[,label.names],y=pred[,1])
ggplot(df,aes(x=x,y=y)) +
geom_point(color='blue',alpha=0.5,shape=20,size=2) +
geom_abline(slope=1,intercept=0,color='black',size=1) +
#scale_y_continuous(limits=c(min(df),max(df)))+
xlab("Actual (Transformed)")+
ylab("Predicted (Transformed)")
}
if (log.pred == FALSE && norm.pred == FALSE){
x = test[,label.names]
y = pred[,1]
}
if (log.pred == TRUE){
x = 10^test[,label.names]
y = 10^pred[,1]
# x = (test[,label.names])^3
# y = (pred[,1])^3
}
if (norm.pred == TRUE){
x = predict(transformation, test[,label.names], inverse = TRUE)
y = predict(transformation, pred[,1], inverse = TRUE)
}
test.mse = mean((x-y)^2)
print (paste(method, subopt, "Test MSE (Org Scale):", test.mse, sep=" "))
test.rmse = sqrt(test.mse)
print (paste(method, subopt, "Test RMSE (Org Scale):", test.rmse, sep=" "))
df=data.frame(x,y)
ggplot(df,aes(x,y)) +
geom_point(color='blue',alpha=0.5,shape=20,size=2) +
geom_abline(slope=c(1+good,1-good,1+ok,1-ok)
,intercept=rep(0,4),color=c('dark green','dark green','dark red','dark red'),size=1,alpha=0.8) +
#scale_y_continuous(limits=c(min(df),max(df)))+
xlab("Actual")+
ylab("Predicted")
}Setup Formulae
n <- names(data.train)
formula <- as.formula(paste(paste(n[n %in% label.names], collapse = " + ")
," ~", paste(n[!n %in% label.names], collapse = " + ")))
grand.mean.formula = as.formula(paste(paste(n[n %in% label.names], collapse = " + ")," ~ 1"))
print(formula)## y3.log ~ PC1 + PC2 + PC3 + PC4 + PC5 + PC6 + PC7 + PC8 + PC9 +
## PC10 + PC11 + PC12 + PC13 + PC14 + PC15 + PC16 + PC17 + PC18 +
## PC19 + PC20 + PC21 + PC22 + PC23 + PC24 + PC25 + PC26 + PC27 +
## PC28 + PC29 + PC30 + PC31 + PC32 + PC33 + PC34 + PC35 + PC36 +
## PC37 + PC38 + PC39 + PC40 + PC41 + PC42 + PC43 + PC44 + PC45 +
## PC46 + PC47 + PC48 + PC49 + PC50 + PC51 + PC52 + PC53 + PC54 +
## PC55 + PC56 + PC57 + PC58 + PC59 + PC60 + PC61 + PC62 + PC63 +
## PC64 + PC65 + PC66 + PC67 + PC68 + PC69 + PC70 + PC71 + PC72 +
## PC73 + PC74 + PC75 + PC76 + PC77 + PC78 + PC79 + PC80 + PC81 +
## PC82 + PC83 + PC84 + PC85 + PC86 + PC87 + PC88 + PC89 + PC90 +
## PC91 + PC92 + PC93 + PC94 + PC95 + PC96 + PC97 + PC98 + PC99 +
## PC100 + PC101 + PC102 + PC103 + PC104 + PC105 + PC106 + PC107 +
## PC108 + PC109 + PC110 + PC111 + PC112 + PC113 + PC114 + PC115 +
## PC116 + PC117 + PC118 + PC119 + PC120 + PC121 + PC122 + PC123 +
## PC124 + PC125 + PC126 + PC127 + PC128 + PC129 + PC130 + PC131 +
## PC132 + PC133 + PC134 + PC135 + PC136 + PC137 + PC138 + PC139 +
## PC140 + PC141 + PC142 + PC143 + PC144 + PC145 + PC146 + PC147 +
## PC148 + PC149 + PC150 + PC151 + PC152 + PC153 + PC154 + PC155 +
## PC156 + PC157 + PC158 + PC159 + PC160 + PC161 + PC162 + PC163 +
## PC164print(grand.mean.formula)## y3.log ~ 1# Update feature.names because we may have transformed some features
feature.names = n[!n %in% label.names]Full Model
model.full = lm(formula , data.train)
summary(model.full)##
## Call:
## lm(formula = formula, data = data.train)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.084858 -0.022051 -0.005534 0.016797 0.183125
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 2.097e+00 4.231e-04 4955.559 < 2e-16 ***
## PC1 -4.836e-04 3.691e-05 -13.100 < 2e-16 ***
## PC2 -9.448e-04 3.746e-05 -25.218 < 2e-16 ***
## PC3 -4.371e-04 3.770e-05 -11.595 < 2e-16 ***
## PC4 -3.491e-04 3.820e-05 -9.140 < 2e-16 ***
## PC5 2.325e-04 3.938e-05 5.904 3.76e-09 ***
## PC6 -9.929e-05 3.936e-05 -2.522 0.011685 *
## PC7 -2.033e-04 4.018e-05 -5.061 4.31e-07 ***
## PC8 -3.725e-05 4.115e-05 -0.905 0.365319
## PC9 -5.154e-05 4.212e-05 -1.224 0.221164
## PC10 -3.929e-06 4.285e-05 -0.092 0.926936
## PC11 -5.386e-04 4.566e-05 -11.796 < 2e-16 ***
## PC12 -5.038e-04 4.810e-05 -10.475 < 2e-16 ***
## PC13 3.436e-04 4.902e-05 7.009 2.70e-12 ***
## PC14 2.536e-04 5.077e-05 4.995 6.08e-07 ***
## PC15 -3.593e-05 5.159e-05 -0.696 0.486188
## PC16 3.542e-04 5.229e-05 6.775 1.38e-11 ***
## PC17 -2.002e-04 5.519e-05 -3.628 0.000289 ***
## PC18 -3.652e-04 5.740e-05 -6.362 2.15e-10 ***
## PC19 4.371e-05 5.810e-05 0.752 0.451900
## PC20 4.121e-04 6.354e-05 6.485 9.64e-11 ***
## PC21 8.386e-05 6.633e-05 1.264 0.206192
## PC22 9.425e-05 1.036e-04 0.910 0.362771
## PC23 2.060e-04 1.278e-04 1.612 0.107072
## PC24 -7.978e-04 1.489e-04 -5.358 8.76e-08 ***
## PC25 2.484e-04 1.685e-04 1.475 0.140375
## PC26 3.859e-04 1.727e-04 2.235 0.025489 *
## PC27 2.691e-04 1.719e-04 1.565 0.117537
## PC28 3.567e-05 1.757e-04 0.203 0.839129
## PC29 3.666e-04 1.917e-04 1.912 0.055931 .
## PC30 -7.683e-05 1.976e-04 -0.389 0.697371
## PC31 -5.625e-05 2.119e-04 -0.265 0.790692
## PC32 -7.103e-04 2.131e-04 -3.333 0.000866 ***
## PC33 7.017e-04 2.176e-04 3.224 0.001270 **
## PC34 1.104e-03 2.302e-04 4.795 1.67e-06 ***
## PC35 7.582e-05 2.455e-04 0.309 0.757414
## PC36 2.574e-05 2.473e-04 0.104 0.917101
## PC37 -3.663e-04 2.568e-04 -1.427 0.153755
## PC38 1.998e-04 2.654e-04 0.753 0.451677
## PC39 -2.058e-04 2.738e-04 -0.751 0.452406
## PC40 -8.637e-05 2.737e-04 -0.316 0.752317
## PC41 -1.524e-04 2.836e-04 -0.537 0.591066
## PC42 -2.202e-04 2.894e-04 -0.761 0.446639
## PC43 1.337e-05 2.887e-04 0.046 0.963070
## PC44 6.412e-04 2.907e-04 2.206 0.027444 *
## PC45 -2.900e-04 2.920e-04 -0.993 0.320687
## PC46 1.042e-04 2.918e-04 0.357 0.721170
## PC47 -4.826e-04 2.925e-04 -1.650 0.099030 .
## PC48 1.024e-04 2.956e-04 0.346 0.729105
## PC49 3.405e-04 2.984e-04 1.141 0.253751
## PC50 7.322e-06 3.012e-04 0.024 0.980608
## PC51 -4.159e-05 3.023e-04 -0.138 0.890557
## PC52 -5.405e-05 3.040e-04 -0.178 0.858906
## PC53 1.362e-04 3.031e-04 0.449 0.653287
## PC54 -4.487e-05 3.087e-04 -0.145 0.884432
## PC55 -4.854e-05 3.126e-04 -0.155 0.876624
## PC56 -1.266e-05 3.123e-04 -0.041 0.967672
## PC57 -7.543e-04 3.146e-04 -2.398 0.016537 *
## PC58 -1.222e-04 3.146e-04 -0.388 0.697747
## PC59 9.754e-04 3.131e-04 3.115 0.001847 **
## PC60 -8.101e-05 3.170e-04 -0.256 0.798317
## PC61 1.282e-04 3.210e-04 0.399 0.689672
## PC62 -3.748e-04 3.231e-04 -1.160 0.246157
## PC63 -6.974e-04 3.213e-04 -2.171 0.030008 *
## PC64 -9.024e-04 3.249e-04 -2.778 0.005493 **
## PC65 -3.464e-05 3.276e-04 -0.106 0.915811
## PC66 -4.220e-04 3.283e-04 -1.286 0.198642
## PC67 2.344e-04 3.271e-04 0.717 0.473691
## PC68 4.975e-04 3.298e-04 1.508 0.131490
## PC69 9.419e-05 3.297e-04 0.286 0.775129
## PC70 1.949e-04 3.312e-04 0.588 0.556264
## PC71 5.198e-04 3.331e-04 1.560 0.118741
## PC72 2.656e-05 3.325e-04 0.080 0.936334
## PC73 4.745e-04 3.353e-04 1.415 0.157123
## PC74 -6.569e-04 3.375e-04 -1.946 0.051682 .
## PC75 -8.762e-04 3.404e-04 -2.574 0.010080 *
## PC76 6.320e-06 3.384e-04 0.019 0.985100
## PC77 4.872e-04 3.390e-04 1.437 0.150734
## PC78 2.820e-04 3.408e-04 0.828 0.407922
## PC79 5.576e-04 3.441e-04 1.620 0.105196
## PC80 -1.334e-04 3.483e-04 -0.383 0.701816
## PC81 7.199e-04 3.446e-04 2.089 0.036750 *
## PC82 4.346e-04 3.524e-04 1.233 0.217601
## PC83 -7.136e-04 3.506e-04 -2.035 0.041852 *
## PC84 8.048e-04 3.517e-04 2.288 0.022157 *
## PC85 1.115e-03 3.563e-04 3.130 0.001758 **
## PC86 -9.678e-05 3.535e-04 -0.274 0.784252
## PC87 1.713e-03 3.537e-04 4.843 1.32e-06 ***
## PC88 -1.142e-03 3.603e-04 -3.170 0.001531 **
## PC89 -5.352e-04 3.592e-04 -1.490 0.136308
## PC90 -5.145e-04 3.599e-04 -1.430 0.152905
## PC91 6.712e-06 3.597e-04 0.019 0.985114
## PC92 2.730e-04 3.569e-04 0.765 0.444363
## PC93 8.076e-05 3.609e-04 0.224 0.822961
## PC94 -9.231e-04 3.633e-04 -2.541 0.011088 *
## PC95 1.072e-04 3.593e-04 0.298 0.765347
## PC96 -4.540e-04 3.669e-04 -1.238 0.215948
## PC97 -5.048e-04 3.644e-04 -1.385 0.166058
## PC98 -4.852e-04 3.638e-04 -1.334 0.182364
## PC99 -4.368e-04 3.650e-04 -1.197 0.231481
## PC100 -5.241e-05 3.654e-04 -0.143 0.885948
## PC101 -1.831e-04 3.669e-04 -0.499 0.617851
## PC102 -5.931e-04 3.658e-04 -1.621 0.105010
## PC103 1.642e-04 3.687e-04 0.445 0.656090
## PC104 -6.728e-04 3.692e-04 -1.823 0.068420 .
## PC105 4.885e-04 3.706e-04 1.318 0.187487
## PC106 1.240e-03 3.716e-04 3.336 0.000856 ***
## PC107 6.011e-04 3.722e-04 1.615 0.106331
## PC108 7.268e-05 3.716e-04 0.196 0.844939
## PC109 5.346e-04 3.721e-04 1.437 0.150860
## PC110 -5.618e-04 3.744e-04 -1.500 0.133597
## PC111 -8.212e-04 3.762e-04 -2.183 0.029067 *
## PC112 -1.273e-04 3.752e-04 -0.339 0.734345
## PC113 3.000e-04 3.772e-04 0.795 0.426421
## PC114 -7.443e-04 3.734e-04 -1.994 0.046256 *
## PC115 -1.656e-03 3.763e-04 -4.400 1.10e-05 ***
## PC116 -1.029e-04 3.796e-04 -0.271 0.786422
## PC117 4.354e-05 3.766e-04 0.116 0.907971
## PC118 7.136e-04 3.792e-04 1.882 0.059899 .
## PC119 -5.390e-04 3.793e-04 -1.421 0.155334
## PC120 2.316e-04 3.777e-04 0.613 0.539853
## PC121 -4.007e-04 3.807e-04 -1.052 0.292664
## PC122 4.944e-04 3.784e-04 1.307 0.191340
## PC123 -5.427e-04 3.819e-04 -1.421 0.155336
## PC124 2.045e-04 3.795e-04 0.539 0.590077
## PC125 4.804e-04 3.826e-04 1.256 0.209334
## PC126 5.539e-05 3.792e-04 0.146 0.883859
## PC127 8.249e-05 3.831e-04 0.215 0.829529
## PC128 -1.001e-03 3.825e-04 -2.618 0.008862 **
## PC129 6.049e-05 3.845e-04 0.157 0.875019
## PC130 4.180e-04 3.826e-04 1.092 0.274734
## PC131 -1.473e-03 3.820e-04 -3.855 0.000117 ***
## PC132 3.136e-04 3.862e-04 0.812 0.416845
## PC133 -1.986e-04 3.855e-04 -0.515 0.606485
## PC134 9.860e-04 3.854e-04 2.558 0.010551 *
## PC135 4.438e-04 3.851e-04 1.152 0.249261
## PC136 5.524e-04 3.881e-04 1.423 0.154713
## PC137 -7.427e-04 3.875e-04 -1.917 0.055339 .
## PC138 5.633e-04 3.893e-04 1.447 0.147996
## PC139 -7.444e-04 3.870e-04 -1.923 0.054476 .
## PC140 -3.928e-04 3.885e-04 -1.011 0.311962
## PC141 3.842e-04 3.866e-04 0.994 0.320412
## PC142 6.662e-05 3.890e-04 0.171 0.864009
## PC143 3.135e-04 3.887e-04 0.806 0.420014
## PC144 1.028e-03 3.901e-04 2.635 0.008443 **
## PC145 1.961e-04 3.900e-04 0.503 0.615043
## PC146 5.962e-04 3.937e-04 1.514 0.129983
## PC147 -2.624e-04 3.916e-04 -0.670 0.502811
## PC148 -5.040e-04 3.911e-04 -1.289 0.197540
## PC149 1.457e-04 3.925e-04 0.371 0.710541
## PC150 6.544e-05 3.936e-04 0.166 0.867974
## PC151 6.700e-04 3.936e-04 1.702 0.088822 .
## PC152 -6.890e-04 3.934e-04 -1.751 0.079947 .
## PC153 4.644e-04 3.968e-04 1.170 0.241953
## PC154 -8.551e-04 3.946e-04 -2.167 0.030272 *
## PC155 1.077e-03 3.955e-04 2.722 0.006505 **
## PC156 1.360e-03 3.960e-04 3.433 0.000602 ***
## PC157 -2.644e-04 3.943e-04 -0.671 0.502549
## PC158 2.302e-05 3.979e-04 0.058 0.953875
## PC159 2.127e-03 3.983e-04 5.340 9.69e-08 ***
## PC160 2.107e-04 3.997e-04 0.527 0.598154
## PC161 3.417e-04 3.968e-04 0.861 0.389252
## PC162 -1.143e-03 4.001e-04 -2.857 0.004295 **
## PC163 6.759e-04 3.976e-04 1.700 0.089230 .
## PC164 2.856e-04 4.011e-04 0.712 0.476382
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.03152 on 5419 degrees of freedom
## Multiple R-squared: 0.2723, Adjusted R-squared: 0.2503
## F-statistic: 12.36 on 164 and 5419 DF, p-value: < 2.2e-16cd.full = plot.diagnostics(model=model.full, train=data.train)
## [1] "Number of data points that have Cook's D > 4/n: 268"
## [1] "Number of data points that have Cook's D > 1: 0"Checking with removal of high influence points
high.cd = names(cd.full[cd.full > 4/nrow(data.train)])
#save dataset with high.cd flagged
t = data.train %>%
rownames_to_column() %>%
mutate(high.cd = ifelse(rowname %in% high.cd,1,0))
#write.csv(t,file='data_high_cd_flag.csv',row.names = F)
###
data.train2 = data.train[!(rownames(data.train)) %in% high.cd,]
model.full2 = lm(formula , data.train2)
summary(model.full2)##
## Call:
## lm(formula = formula, data = data.train2)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.05672 -0.01919 -0.00363 0.01675 0.08122
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 2.093e+00 3.531e-04 5928.987 < 2e-16 ***
## PC1 -5.034e-04 3.140e-05 -16.030 < 2e-16 ***
## PC2 -9.257e-04 3.131e-05 -29.568 < 2e-16 ***
## PC3 -4.501e-04 3.167e-05 -14.211 < 2e-16 ***
## PC4 -3.651e-04 3.191e-05 -11.443 < 2e-16 ***
## PC5 2.259e-04 3.314e-05 6.816 1.04e-11 ***
## PC6 -7.324e-05 3.293e-05 -2.224 0.026187 *
## PC7 -2.212e-04 3.361e-05 -6.581 5.12e-11 ***
## PC8 -3.088e-05 3.449e-05 -0.895 0.370608
## PC9 -7.797e-06 3.523e-05 -0.221 0.824864
## PC10 7.869e-06 3.591e-05 0.219 0.826579
## PC11 -6.081e-04 3.812e-05 -15.950 < 2e-16 ***
## PC12 -5.098e-04 4.010e-05 -12.714 < 2e-16 ***
## PC13 3.338e-04 4.097e-05 8.149 4.57e-16 ***
## PC14 2.368e-04 4.226e-05 5.605 2.19e-08 ***
## PC15 -5.593e-05 4.314e-05 -1.296 0.194885
## PC16 3.220e-04 4.363e-05 7.380 1.84e-13 ***
## PC17 -2.158e-04 4.599e-05 -4.691 2.79e-06 ***
## PC18 -3.629e-04 4.789e-05 -7.577 4.15e-14 ***
## PC19 7.338e-05 4.852e-05 1.513 0.130449
## PC20 4.288e-04 5.301e-05 8.090 7.38e-16 ***
## PC21 9.219e-05 5.537e-05 1.665 0.095973 .
## PC22 1.381e-04 8.630e-05 1.600 0.109588
## PC23 2.000e-04 1.082e-04 1.848 0.064598 .
## PC24 -8.489e-04 1.246e-04 -6.812 1.07e-11 ***
## PC25 3.575e-04 1.417e-04 2.523 0.011669 *
## PC26 3.303e-04 1.444e-04 2.287 0.022250 *
## PC27 1.512e-04 1.445e-04 1.046 0.295399
## PC28 1.902e-05 1.477e-04 0.129 0.897552
## PC29 4.153e-04 1.601e-04 2.595 0.009498 **
## PC30 -5.140e-05 1.662e-04 -0.309 0.757196
## PC31 -1.370e-04 1.786e-04 -0.767 0.443107
## PC32 -6.672e-04 1.785e-04 -3.739 0.000187 ***
## PC33 2.763e-04 1.840e-04 1.502 0.133266
## PC34 1.059e-03 1.922e-04 5.511 3.75e-08 ***
## PC35 2.186e-04 2.076e-04 1.053 0.292483
## PC36 -6.446e-05 2.078e-04 -0.310 0.756452
## PC37 -5.049e-04 2.149e-04 -2.350 0.018810 *
## PC38 1.114e-04 2.220e-04 0.502 0.615826
## PC39 -1.252e-04 2.388e-04 -0.524 0.600011
## PC40 -1.215e-04 2.316e-04 -0.525 0.599779
## PC41 -3.360e-04 2.397e-04 -1.402 0.160972
## PC42 1.117e-04 2.438e-04 0.458 0.646730
## PC43 2.907e-04 2.436e-04 1.194 0.232721
## PC44 3.989e-04 2.486e-04 1.605 0.108606
## PC45 -1.190e-04 2.453e-04 -0.485 0.627501
## PC46 1.418e-04 2.466e-04 0.575 0.565425
## PC47 -4.521e-04 2.461e-04 -1.837 0.066253 .
## PC48 1.111e-04 2.488e-04 0.447 0.655212
## PC49 4.302e-04 2.515e-04 1.710 0.087267 .
## PC50 -1.990e-04 2.545e-04 -0.782 0.434306
## PC51 1.372e-04 2.567e-04 0.535 0.592990
## PC52 -2.241e-04 2.564e-04 -0.874 0.382227
## PC53 1.746e-04 2.557e-04 0.683 0.494703
## PC54 -3.477e-04 2.627e-04 -1.324 0.185712
## PC55 -4.148e-04 2.638e-04 -1.573 0.115894
## PC56 1.240e-04 2.660e-04 0.466 0.640965
## PC57 -7.998e-04 2.657e-04 -3.010 0.002625 **
## PC58 -4.297e-04 2.671e-04 -1.609 0.107752
## PC59 1.015e-03 2.661e-04 3.813 0.000139 ***
## PC60 -3.669e-04 2.687e-04 -1.366 0.172155
## PC61 -2.166e-05 2.694e-04 -0.080 0.935928
## PC62 -1.893e-04 2.724e-04 -0.695 0.487022
## PC63 -5.771e-04 2.699e-04 -2.138 0.032562 *
## PC64 -7.240e-04 2.733e-04 -2.649 0.008094 **
## PC65 -1.539e-04 2.756e-04 -0.558 0.576533
## PC66 -1.636e-04 2.781e-04 -0.588 0.556342
## PC67 1.505e-04 2.781e-04 0.541 0.588459
## PC68 6.390e-04 2.789e-04 2.291 0.021990 *
## PC69 3.767e-04 2.781e-04 1.354 0.175687
## PC70 3.950e-04 2.766e-04 1.428 0.153317
## PC71 3.641e-04 2.791e-04 1.304 0.192177
## PC72 -1.055e-04 2.797e-04 -0.377 0.706032
## PC73 4.437e-04 2.800e-04 1.585 0.113072
## PC74 -2.907e-04 2.848e-04 -1.021 0.307478
## PC75 -6.510e-04 2.870e-04 -2.268 0.023341 *
## PC76 -2.030e-04 2.835e-04 -0.716 0.473992
## PC77 3.497e-04 2.840e-04 1.231 0.218286
## PC78 -6.564e-05 2.866e-04 -0.229 0.818839
## PC79 7.159e-04 2.891e-04 2.476 0.013315 *
## PC80 -1.919e-04 2.907e-04 -0.660 0.509199
## PC81 8.874e-04 2.882e-04 3.080 0.002084 **
## PC82 3.492e-04 2.954e-04 1.182 0.237253
## PC83 -6.782e-04 2.963e-04 -2.289 0.022115 *
## PC84 7.847e-04 2.961e-04 2.650 0.008068 **
## PC85 1.380e-03 3.013e-04 4.581 4.75e-06 ***
## PC86 9.588e-05 2.964e-04 0.324 0.746319
## PC87 1.481e-03 2.955e-04 5.013 5.55e-07 ***
## PC88 -9.719e-04 3.015e-04 -3.223 0.001276 **
## PC89 -3.580e-04 3.014e-04 -1.188 0.235042
## PC90 -3.864e-04 3.019e-04 -1.280 0.200633
## PC91 -1.221e-04 2.998e-04 -0.407 0.683912
## PC92 4.982e-04 2.978e-04 1.673 0.094410 .
## PC93 -2.352e-04 3.036e-04 -0.775 0.438562
## PC94 -7.713e-04 3.045e-04 -2.533 0.011338 *
## PC95 2.487e-04 3.029e-04 0.821 0.411519
## PC96 -2.991e-04 3.071e-04 -0.974 0.330041
## PC97 -3.630e-04 3.045e-04 -1.192 0.233365
## PC98 -5.363e-04 3.041e-04 -1.764 0.077835 .
## PC99 -1.667e-04 3.047e-04 -0.547 0.584256
## PC100 -4.433e-05 3.048e-04 -0.145 0.884353
## PC101 -3.681e-04 3.069e-04 -1.199 0.230501
## PC102 -4.342e-04 3.055e-04 -1.421 0.155281
## PC103 -9.655e-05 3.088e-04 -0.313 0.754536
## PC104 -6.635e-04 3.073e-04 -2.159 0.030875 *
## PC105 6.801e-04 3.098e-04 2.195 0.028181 *
## PC106 1.154e-03 3.094e-04 3.729 0.000194 ***
## PC107 6.590e-04 3.127e-04 2.108 0.035102 *
## PC108 1.136e-05 3.102e-04 0.037 0.970776
## PC109 4.196e-04 3.115e-04 1.347 0.178116
## PC110 -5.413e-04 3.133e-04 -1.727 0.084144 .
## PC111 -9.389e-04 3.147e-04 -2.984 0.002861 **
## PC112 -8.764e-05 3.134e-04 -0.280 0.779752
## PC113 1.350e-04 3.150e-04 0.429 0.668236
## PC114 -8.034e-04 3.123e-04 -2.573 0.010123 *
## PC115 -1.890e-03 3.146e-04 -6.010 1.99e-09 ***
## PC116 -9.974e-07 3.173e-04 -0.003 0.997492
## PC117 1.906e-04 3.148e-04 0.605 0.544903
## PC118 4.988e-04 3.163e-04 1.577 0.114890
## PC119 -3.598e-04 3.170e-04 -1.135 0.256510
## PC120 1.076e-04 3.164e-04 0.340 0.733921
## PC121 -6.644e-04 3.173e-04 -2.094 0.036317 *
## PC122 3.526e-04 3.154e-04 1.118 0.263674
## PC123 -5.212e-04 3.196e-04 -1.631 0.102958
## PC124 -2.618e-04 3.177e-04 -0.824 0.409991
## PC125 6.122e-04 3.197e-04 1.915 0.055558 .
## PC126 3.150e-05 3.167e-04 0.099 0.920752
## PC127 -1.166e-04 3.195e-04 -0.365 0.715173
## PC128 -9.783e-04 3.193e-04 -3.064 0.002193 **
## PC129 -2.623e-04 3.233e-04 -0.811 0.417187
## PC130 3.091e-04 3.193e-04 0.968 0.332960
## PC131 -8.760e-04 3.194e-04 -2.743 0.006115 **
## PC132 2.770e-04 3.227e-04 0.858 0.390718
## PC133 -2.061e-04 3.238e-04 -0.636 0.524486
## PC134 7.610e-04 3.222e-04 2.362 0.018219 *
## PC135 1.727e-04 3.212e-04 0.538 0.590802
## PC136 6.016e-04 3.252e-04 1.850 0.064343 .
## PC137 -9.984e-04 3.234e-04 -3.087 0.002029 **
## PC138 6.008e-04 3.267e-04 1.839 0.065932 .
## PC139 -4.006e-04 3.240e-04 -1.236 0.216373
## PC140 -5.621e-04 3.247e-04 -1.731 0.083454 .
## PC141 5.247e-04 3.235e-04 1.622 0.104854
## PC142 2.124e-04 3.248e-04 0.654 0.513025
## PC143 3.476e-04 3.242e-04 1.072 0.283636
## PC144 7.608e-04 3.261e-04 2.333 0.019666 *
## PC145 4.973e-04 3.258e-04 1.526 0.126971
## PC146 9.733e-04 3.290e-04 2.958 0.003107 **
## PC147 -1.885e-04 3.284e-04 -0.574 0.565982
## PC148 -4.102e-04 3.252e-04 -1.261 0.207324
## PC149 -1.014e-04 3.283e-04 -0.309 0.757431
## PC150 3.459e-04 3.293e-04 1.050 0.293564
## PC151 7.120e-04 3.276e-04 2.174 0.029787 *
## PC152 -4.921e-04 3.285e-04 -1.498 0.134224
## PC153 2.756e-04 3.308e-04 0.833 0.404865
## PC154 -5.758e-04 3.301e-04 -1.745 0.081113 .
## PC155 8.040e-04 3.301e-04 2.436 0.014880 *
## PC156 1.114e-03 3.318e-04 3.357 0.000794 ***
## PC157 -4.443e-06 3.294e-04 -0.013 0.989239
## PC158 9.148e-05 3.326e-04 0.275 0.783298
## PC159 1.606e-03 3.321e-04 4.834 1.38e-06 ***
## PC160 1.774e-04 3.360e-04 0.528 0.597676
## PC161 -5.438e-05 3.318e-04 -0.164 0.869818
## PC162 -1.072e-03 3.337e-04 -3.214 0.001318 **
## PC163 6.251e-04 3.330e-04 1.877 0.060568 .
## PC164 3.103e-04 3.351e-04 0.926 0.354463
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.02562 on 5151 degrees of freedom
## Multiple R-squared: 0.3602, Adjusted R-squared: 0.3398
## F-statistic: 17.68 on 164 and 5151 DF, p-value: < 2.2e-16cd.full2 = plot.diagnostics(model.full2, data.train2)
## [1] "Number of data points that have Cook's D > 4/n: 222"
## [1] "Number of data points that have Cook's D > 1: 0"# much more normal residuals than before.
# Checking to see if distributions are different and if so whcih variables
# High Leverage Plot
plotData = data.train %>%
rownames_to_column() %>%
mutate(type=ifelse(rowname %in% high.cd,'High','Normal')) %>%
dplyr::select(type,target=one_of(label.names))
ggplot(data=plotData, aes(x=type,y=target)) +
geom_boxplot(fill='light blue',outlier.shape=NA) +
scale_y_continuous(name="Target Variable Values",label=scales::comma_format(accuracy=.1)) +
theme_light() +
ggtitle('Distribution of High Leverage Points and Normal Points')
# 2 sample t-tests
plotData = data.train %>%
rownames_to_column() %>%
mutate(type=ifelse(rowname %in% high.cd,'High','Normal')) %>%
dplyr::select(type,one_of(feature.names))
comp.test = lapply(dplyr::select(plotData, one_of(feature.names))
, function(x) t.test(x ~ plotData$type, var.equal = TRUE))
sig.comp = list.filter(comp.test, p.value < 0.05)
sapply(sig.comp, function(x) x[['p.value']])## PC1 PC6 PC11 PC23 PC25 PC26 PC28 PC31 PC33
## 1.114429e-04 2.900174e-02 3.453559e-05 1.870981e-03 1.469834e-03 4.459918e-03 7.170787e-03 1.788345e-03 1.625765e-04
## PC40 PC41 PC42 PC45 PC57 PC58 PC75 PC131 PC161
## 4.821597e-02 1.220165e-02 4.394526e-02 4.240457e-02 3.886254e-02 1.006641e-02 1.418026e-02 4.893946e-02 3.717655e-02mm = melt(plotData, id=c('type')) %>% filter(variable %in% names(sig.comp))
ggplot(mm,aes(x=type, y=value)) +
geom_boxplot()+
facet_wrap(~variable, ncol=5, scales = 'free_y') +
scale_y_continuous(name="values",label=scales::comma_format(accuracy=.1)) +
ggtitle('Distribution of High Leverage Points and Normal Points')
# Distribution (box) Plots
mm = melt(plotData, id=c('type'))
ggplot(mm,aes(x=type, y=value)) +
geom_boxplot()+
facet_wrap(~variable, ncol=8, scales = 'free_y') +
scale_y_continuous(name="values",label=scales::comma_format(accuracy=.1)) +
ggtitle('Distribution of High Leverage Points and Normal Points')
Grand Means Model
model.null = lm(grand.mean.formula, data.train)
summary(model.null)##
## Call:
## lm(formula = grand.mean.formula, data = data.train)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.114932 -0.023964 -0.003377 0.020682 0.190380
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 2.0968082 0.0004871 4304 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.0364 on 5583 degrees of freedomVariable Selection
Basic: http://www.stat.columbia.edu/~martin/W2024/R10.pdf Cross Validation + Other Metrics: http://www.sthda.com/english/articles/37-model-selection-essentials-in-r/154-stepwise-regression-essentials-in-r/
Forward Selection with CV
Train
if (algo.forward.caret == TRUE){
set.seed(1)
returned = train.caret.glmselect(formula = formula
, data = data.train
, method = "leapForward"
, feature.names = feature.names)
model.forward = returned$model
id = returned$id
}## Aggregating results
## Selecting tuning parameters
## Fitting nvmax = 110 on full training set
## [1] "All models results"
## nvmax RMSE Rsquared MAE RMSESD RsquaredSD MAESD
## 1 1 0.03477291 0.08867342 0.02692328 0.001241527 0.02694524 0.0007080957
## 2 2 0.03430526 0.11280445 0.02659499 0.001382164 0.03177241 0.0008448670
## 3 3 0.03397028 0.13012834 0.02629226 0.001480367 0.03628599 0.0009228758
## 4 4 0.03357202 0.15065682 0.02594497 0.001495727 0.03862072 0.0008898614
## 5 5 0.03329810 0.16453122 0.02572753 0.001417074 0.04025876 0.0008731997
## 6 6 0.03307787 0.17576857 0.02556677 0.001504730 0.04328083 0.0009446991
## 7 7 0.03306407 0.17615661 0.02557869 0.001452171 0.03968875 0.0009114778
## 8 8 0.03295739 0.18134530 0.02547827 0.001388292 0.03792930 0.0008274437
## 9 9 0.03287939 0.18540661 0.02543399 0.001348211 0.03725882 0.0008444702
## 10 10 0.03275470 0.19146665 0.02537654 0.001412011 0.03832877 0.0008875603
## 11 11 0.03263033 0.19759284 0.02525113 0.001364011 0.03659311 0.0008756810
## 12 12 0.03257233 0.20048903 0.02523311 0.001354071 0.03672316 0.0008542372
## 13 13 0.03251170 0.20352002 0.02521402 0.001350424 0.03679330 0.0008351289
## 14 14 0.03244689 0.20662371 0.02517335 0.001343122 0.03644511 0.0008246527
## 15 15 0.03237508 0.21024129 0.02509782 0.001358417 0.03834147 0.0008435020
## 16 16 0.03229967 0.21374950 0.02503485 0.001309698 0.03485740 0.0007989186
## 17 17 0.03220992 0.21809658 0.02496221 0.001315084 0.03542000 0.0007926923
## 18 18 0.03211348 0.22278477 0.02488082 0.001329096 0.03586858 0.0008024469
## 19 19 0.03212837 0.22212585 0.02490779 0.001341751 0.03746177 0.0008003150
## 20 20 0.03213781 0.22162102 0.02492734 0.001312032 0.03662545 0.0008052886
## 21 21 0.03213292 0.22181018 0.02493871 0.001309637 0.03648529 0.0008097871
## 22 22 0.03216415 0.22035170 0.02496546 0.001314688 0.03606900 0.0007887597
## 23 23 0.03218004 0.21978765 0.02499320 0.001345886 0.03797314 0.0008001592
## 24 24 0.03217962 0.21989948 0.02499754 0.001375751 0.03808737 0.0008155772
## 25 25 0.03216149 0.22080358 0.02497778 0.001375812 0.03724828 0.0008036009
## 26 26 0.03212754 0.22246909 0.02494849 0.001386134 0.03808964 0.0008222826
## 27 27 0.03212246 0.22285030 0.02494429 0.001391138 0.03842345 0.0008183642
## 28 28 0.03212054 0.22291448 0.02492916 0.001365167 0.03745133 0.0007960654
## 29 29 0.03213711 0.22235720 0.02493668 0.001391574 0.03860505 0.0008025450
## 30 30 0.03212025 0.22308219 0.02492951 0.001388672 0.03889539 0.0008091720
## 31 31 0.03208205 0.22473091 0.02492124 0.001375580 0.03945830 0.0008133107
## 32 32 0.03207245 0.22525612 0.02491403 0.001391883 0.04080784 0.0008220509
## 33 33 0.03205101 0.22624599 0.02491031 0.001414465 0.04119436 0.0008491636
## 34 34 0.03204038 0.22659548 0.02490480 0.001410639 0.03965959 0.0008407845
## 35 35 0.03203920 0.22676001 0.02490051 0.001440626 0.04120706 0.0008483916
## 36 36 0.03204357 0.22658775 0.02490517 0.001438758 0.04130931 0.0008377819
## 37 37 0.03205419 0.22603709 0.02492207 0.001411729 0.03992416 0.0008175293
## 38 38 0.03205665 0.22597332 0.02491471 0.001416434 0.04021166 0.0008146284
## 39 39 0.03205383 0.22615437 0.02489986 0.001412482 0.04047099 0.0008314997
## 40 40 0.03204261 0.22671345 0.02489137 0.001406340 0.04047229 0.0008341381
## 41 41 0.03204194 0.22681627 0.02489759 0.001388689 0.04040147 0.0008204343
## 42 42 0.03206928 0.22555906 0.02490955 0.001403987 0.04095464 0.0008232951
## 43 43 0.03206459 0.22584693 0.02490599 0.001421581 0.04094682 0.0008400139
## 44 44 0.03208054 0.22514515 0.02491116 0.001424649 0.04083853 0.0008497526
## 45 45 0.03209622 0.22450274 0.02491986 0.001435414 0.04092379 0.0008529708
## 46 46 0.03209956 0.22434653 0.02491289 0.001441379 0.04081349 0.0008540198
## 47 47 0.03209368 0.22467742 0.02492201 0.001431325 0.04050589 0.0008697596
## 48 48 0.03209705 0.22454075 0.02492311 0.001417384 0.04056557 0.0008803787
## 49 49 0.03210387 0.22430303 0.02493020 0.001422928 0.04096309 0.0008941356
## 50 50 0.03210893 0.22418459 0.02494379 0.001433631 0.04040852 0.0008870796
## 51 51 0.03211367 0.22395579 0.02494293 0.001410433 0.03937421 0.0008857971
## 52 52 0.03210812 0.22425578 0.02493588 0.001435740 0.03983291 0.0008981506
## 53 53 0.03213614 0.22308290 0.02495360 0.001421114 0.03948345 0.0008819039
## 54 54 0.03211956 0.22381943 0.02493168 0.001419330 0.03933501 0.0008807096
## 55 55 0.03212483 0.22349935 0.02494206 0.001407913 0.03907454 0.0008742864
## 56 56 0.03211988 0.22366659 0.02493888 0.001390261 0.03823314 0.0008750261
## 57 57 0.03211959 0.22379649 0.02495186 0.001411565 0.03936397 0.0008980209
## 58 58 0.03211239 0.22416596 0.02494613 0.001415538 0.03898629 0.0008897171
## 59 59 0.03213626 0.22315172 0.02496361 0.001426162 0.03930488 0.0008823017
## 60 60 0.03212702 0.22361709 0.02494877 0.001416076 0.03903726 0.0008765432
## 61 61 0.03210096 0.22489597 0.02492605 0.001439037 0.04028342 0.0008964696
## 62 62 0.03210095 0.22492682 0.02493399 0.001438011 0.04009270 0.0008861095
## 63 63 0.03209720 0.22513292 0.02493683 0.001431737 0.04002607 0.0008904852
## 64 64 0.03208974 0.22549962 0.02494178 0.001448366 0.04069485 0.0009083664
## 65 65 0.03207369 0.22624304 0.02492354 0.001446947 0.04059217 0.0009086123
## 66 66 0.03208122 0.22592667 0.02492976 0.001445905 0.04036995 0.0009069383
## 67 67 0.03208651 0.22577119 0.02492386 0.001467726 0.04172392 0.0009210062
## 68 68 0.03208296 0.22600295 0.02492151 0.001460244 0.04121981 0.0009289866
## 69 69 0.03208365 0.22601794 0.02492840 0.001460697 0.04108034 0.0009501540
## 70 70 0.03206845 0.22667152 0.02491273 0.001459194 0.04109847 0.0009502501
## 71 71 0.03207832 0.22630140 0.02492499 0.001464890 0.04120853 0.0009532068
## 72 72 0.03207177 0.22660594 0.02492913 0.001478852 0.04139493 0.0009545841
## 73 73 0.03207884 0.22627552 0.02493485 0.001469068 0.04036586 0.0009346723
## 74 74 0.03207339 0.22659491 0.02493149 0.001463956 0.04019921 0.0009356794
## 75 75 0.03206829 0.22688087 0.02492237 0.001474386 0.04053992 0.0009318329
## 76 76 0.03206466 0.22708593 0.02491883 0.001467288 0.04050069 0.0009265166
## 77 77 0.03206180 0.22727944 0.02491406 0.001478382 0.04097980 0.0009401027
## 78 78 0.03206572 0.22712987 0.02492160 0.001490180 0.04163382 0.0009654985
## 79 79 0.03206475 0.22718500 0.02491609 0.001497328 0.04179955 0.0009693802
## 80 80 0.03205612 0.22759815 0.02490265 0.001502915 0.04195964 0.0009844772
## 81 81 0.03205316 0.22773533 0.02489855 0.001505466 0.04189693 0.0009817560
## 82 82 0.03204938 0.22791273 0.02489471 0.001512247 0.04196206 0.0009838911
## 83 83 0.03202912 0.22879362 0.02487673 0.001523331 0.04242504 0.0009910866
## 84 84 0.03202471 0.22898440 0.02487507 0.001511604 0.04207290 0.0009775806
## 85 85 0.03201666 0.22929142 0.02486827 0.001505642 0.04167351 0.0009698796
## 86 86 0.03202020 0.22919691 0.02487510 0.001505318 0.04148260 0.0009797739
## 87 87 0.03202049 0.22920823 0.02486943 0.001513029 0.04154932 0.0009816358
## 88 88 0.03200355 0.22995467 0.02485315 0.001509959 0.04129271 0.0009839007
## 89 89 0.03199615 0.23030017 0.02485287 0.001494104 0.04064939 0.0009802010
## 90 90 0.03199122 0.23047923 0.02485128 0.001497331 0.04054004 0.0009862718
## 91 91 0.03199047 0.23048736 0.02484950 0.001492883 0.04004239 0.0009767817
## 92 92 0.03198692 0.23068711 0.02485162 0.001503173 0.04046130 0.0009824728
## 93 93 0.03199563 0.23033078 0.02486512 0.001501557 0.04050489 0.0009831600
## 94 94 0.03199797 0.23019872 0.02487101 0.001491583 0.03987966 0.0009803743
## 95 95 0.03199335 0.23047009 0.02486655 0.001497794 0.03984521 0.0009876680
## 96 96 0.03199746 0.23032450 0.02486091 0.001503405 0.04010818 0.0009930313
## 97 97 0.03199439 0.23046756 0.02485649 0.001523995 0.04066097 0.0010012025
## 98 98 0.03199664 0.23033950 0.02485843 0.001524000 0.04051750 0.0009991824
## 99 99 0.03199963 0.23022039 0.02485740 0.001532018 0.04062958 0.0010081561
## 100 100 0.03199394 0.23046923 0.02485372 0.001528450 0.04054620 0.0010078808
## 101 101 0.03199103 0.23058576 0.02485530 0.001521794 0.03996122 0.0009983527
## 102 102 0.03199172 0.23056819 0.02485462 0.001524524 0.04016561 0.0009981462
## 103 103 0.03197871 0.23114909 0.02484476 0.001525203 0.04043456 0.0009987292
## 104 104 0.03197442 0.23134640 0.02484161 0.001529584 0.04039329 0.0010055524
## 105 105 0.03197723 0.23123436 0.02483659 0.001532022 0.04045956 0.0010119291
## 106 106 0.03197358 0.23140859 0.02483619 0.001533794 0.04089880 0.0010164772
## 107 107 0.03197305 0.23144303 0.02483680 0.001539769 0.04097211 0.0010192725
## 108 108 0.03197029 0.23154870 0.02483612 0.001541826 0.04123377 0.0010298468
## 109 109 0.03197142 0.23147689 0.02483488 0.001538675 0.04102166 0.0010223219
## 110 110 0.03196823 0.23159643 0.02482476 0.001529341 0.04067338 0.0010134655
## 111 111 0.03197336 0.23138431 0.02482805 0.001533506 0.04106195 0.0010142136
## 112 112 0.03197136 0.23152606 0.02482293 0.001534555 0.04113854 0.0010085159
## 113 113 0.03197461 0.23137605 0.02482809 0.001531756 0.04104360 0.0010053112
## 114 114 0.03197604 0.23132361 0.02482609 0.001528680 0.04094427 0.0010053142
## 115 115 0.03197837 0.23122685 0.02483174 0.001530312 0.04067612 0.0010056174
## 116 116 0.03197979 0.23118245 0.02483204 0.001530900 0.04075648 0.0010049239
## 117 117 0.03198423 0.23099071 0.02483741 0.001524602 0.04059462 0.0010025404
## 118 118 0.03198748 0.23086744 0.02484001 0.001524930 0.04057813 0.0009998928
## 119 119 0.03199519 0.23053784 0.02484830 0.001525864 0.04054937 0.0010003865
## 120 120 0.03198976 0.23078268 0.02484224 0.001526166 0.04039139 0.0010019231
## 121 121 0.03198885 0.23082304 0.02484123 0.001523881 0.04011096 0.0009993482
## 122 122 0.03199615 0.23052753 0.02484857 0.001524203 0.04019993 0.0009978955
## 123 123 0.03199822 0.23042646 0.02484948 0.001520157 0.04005783 0.0009911628
## 124 124 0.03200088 0.23032480 0.02485123 0.001522284 0.04027961 0.0009901903
## 125 125 0.03199964 0.23036807 0.02484816 0.001522779 0.04032824 0.0009907574
## 126 126 0.03200003 0.23038047 0.02484480 0.001523229 0.04039877 0.0009974876
## 127 127 0.03200552 0.23015056 0.02484835 0.001524890 0.04057208 0.0009998711
## 128 128 0.03200849 0.23002288 0.02485181 0.001528606 0.04074557 0.0010019670
## 129 129 0.03200626 0.23011574 0.02484972 0.001527317 0.04070563 0.0010032649
## 130 130 0.03200723 0.23010004 0.02485102 0.001527097 0.04074447 0.0010069934
## 131 131 0.03201137 0.22992104 0.02485348 0.001528458 0.04078396 0.0010063671
## 132 132 0.03200983 0.22999040 0.02485419 0.001530295 0.04084604 0.0010071048
## 133 133 0.03201344 0.22984440 0.02485941 0.001533387 0.04108508 0.0010103116
## 134 134 0.03201365 0.22984281 0.02486109 0.001534540 0.04101024 0.0010112674
## 135 135 0.03201087 0.22997089 0.02485950 0.001532274 0.04101278 0.0010095930
## 136 136 0.03200837 0.23008806 0.02485724 0.001532864 0.04107810 0.0010121125
## 137 137 0.03200963 0.23002545 0.02485927 0.001531753 0.04099892 0.0010112603
## 138 138 0.03201521 0.22978175 0.02486343 0.001529153 0.04079978 0.0010098656
## 139 139 0.03201599 0.22975859 0.02486464 0.001531158 0.04090856 0.0010121685
## 140 140 0.03201472 0.22979583 0.02486228 0.001529158 0.04087428 0.0010116301
## 141 141 0.03201762 0.22966093 0.02486391 0.001527853 0.04080573 0.0010124458
## 142 142 0.03201652 0.22972501 0.02486216 0.001529424 0.04087584 0.0010118080
## 143 143 0.03201593 0.22975229 0.02486209 0.001532447 0.04099954 0.0010146881
## 144 144 0.03201685 0.22972231 0.02486141 0.001533976 0.04103142 0.0010153620
## 145 145 0.03201745 0.22970677 0.02486172 0.001533723 0.04103160 0.0010156287
## 146 146 0.03201830 0.22966711 0.02486291 0.001532618 0.04100083 0.0010146294
## 147 147 0.03201959 0.22961148 0.02486442 0.001533643 0.04103777 0.0010153806
## 148 148 0.03202083 0.22956075 0.02486592 0.001532662 0.04098088 0.0010129589
## 149 149 0.03202186 0.22952486 0.02486700 0.001534175 0.04101414 0.0010138945
## 150 150 0.03202152 0.22954559 0.02486707 0.001536138 0.04108821 0.0010166699
## 151 151 0.03202283 0.22948672 0.02486717 0.001536222 0.04104770 0.0010162828
## 152 152 0.03202294 0.22948434 0.02486700 0.001536319 0.04107400 0.0010171523
## 153 153 0.03202280 0.22949054 0.02486656 0.001536304 0.04106531 0.0010170736
## 154 154 0.03202125 0.22955754 0.02486463 0.001536783 0.04108383 0.0010179749
## 155 155 0.03202162 0.22953372 0.02486414 0.001537131 0.04110253 0.0010177444
## 156 156 0.03202231 0.22950264 0.02486497 0.001537206 0.04114068 0.0010179990
## 157 157 0.03202253 0.22949211 0.02486553 0.001535889 0.04110959 0.0010174766
## 158 158 0.03202272 0.22948379 0.02486528 0.001536237 0.04110658 0.0010176311
## 159 159 0.03202318 0.22946528 0.02486570 0.001535923 0.04109475 0.0010176663
## 160 160 0.03202287 0.22948068 0.02486567 0.001536339 0.04111202 0.0010178004
## 161 161 0.03202274 0.22948616 0.02486571 0.001536346 0.04111327 0.0010175342
## 162 162 0.03202292 0.22947816 0.02486583 0.001536473 0.04111787 0.0010178911
## 163 163 0.03202284 0.22948087 0.02486558 0.001536518 0.04112019 0.0010179683
## 164 164 0.03202267 0.22948948 0.02486541 0.001536708 0.04113085 0.0010181546
## [1] "Best Model"
## nvmax
## 110 110
## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
## [1] "Coefficients of final model:"
## Estimate 2.5 % 97.5 %
## (Intercept) 2.096921e+00 2.096096e+00 2.097746e+00
## PC1 -4.820829e-04 -5.540102e-04 -4.101556e-04
## PC2 -9.439758e-04 -1.017022e-03 -8.709292e-04
## PC3 -4.376253e-04 -5.110635e-04 -3.641872e-04
## PC4 -3.485515e-04 -4.229921e-04 -2.741108e-04
## PC5 2.305793e-04 1.538579e-04 3.073007e-04
## PC6 -9.916849e-05 -1.759127e-04 -2.242430e-05
## PC7 -2.034675e-04 -2.818330e-04 -1.251020e-04
## PC8 -3.732177e-05 -1.175225e-04 4.287892e-05
## PC9 -5.229907e-05 -1.344202e-04 2.982208e-05
## PC11 -5.388938e-04 -6.279221e-04 -4.498656e-04
## PC12 -5.049829e-04 -5.988052e-04 -4.111606e-04
## PC13 3.431100e-04 2.475465e-04 4.386736e-04
## PC14 2.527666e-04 1.537902e-04 3.517430e-04
## PC16 3.558417e-04 2.538653e-04 4.578182e-04
## PC17 -1.998529e-04 -3.074757e-04 -9.223015e-05
## PC18 -3.654310e-04 -4.773739e-04 -2.534881e-04
## PC19 4.317135e-05 -7.010991e-05 1.564526e-04
## PC20 4.101492e-04 2.862502e-04 5.340482e-04
## PC21 8.180626e-05 -4.747785e-05 2.110904e-04
## PC22 9.282618e-05 -1.090969e-04 2.947493e-04
## PC23 2.053985e-04 -4.390229e-05 4.546993e-04
## PC24 -7.967536e-04 -1.087088e-03 -5.064190e-04
## PC25 2.524151e-04 -7.599813e-05 5.808283e-04
## PC26 3.833125e-04 4.667886e-05 7.199461e-04
## PC27 2.715470e-04 -6.361989e-05 6.067139e-04
## PC29 3.679176e-04 -5.941506e-06 7.417766e-04
## PC32 -7.123956e-04 -1.128028e-03 -2.967633e-04
## PC33 7.039065e-04 2.795701e-04 1.128243e-03
## PC34 1.099756e-03 6.511037e-04 1.548408e-03
## PC37 -3.603607e-04 -8.610729e-04 1.403515e-04
## PC38 2.032648e-04 -3.141561e-04 7.206857e-04
## PC39 -2.080906e-04 -7.413170e-04 3.251358e-04
## PC42 -2.251949e-04 -7.889242e-04 3.385343e-04
## PC44 6.421781e-04 7.553640e-05 1.208820e-03
## PC45 -2.968457e-04 -8.659781e-04 2.722868e-04
## PC47 -4.846403e-04 -1.054791e-03 8.551069e-05
## PC49 3.431287e-04 -2.384184e-04 9.246758e-04
## PC57 -7.572567e-04 -1.370314e-03 -1.441993e-04
## PC59 9.818223e-04 3.716729e-04 1.591972e-03
## PC62 -3.745738e-04 -1.004500e-03 2.553524e-04
## PC63 -7.029549e-04 -1.328927e-03 -7.698276e-05
## PC64 -9.023538e-04 -1.535550e-03 -2.691578e-04
## PC66 -4.331374e-04 -1.073173e-03 2.068977e-04
## PC68 4.950411e-04 -1.474936e-04 1.137576e-03
## PC71 5.213597e-04 -1.282802e-04 1.171000e-03
## PC73 4.679612e-04 -1.857211e-04 1.121643e-03
## PC74 -6.580551e-04 -1.315861e-03 -2.495721e-07
## PC75 -8.829193e-04 -1.546441e-03 -2.193976e-04
## PC77 4.911264e-04 -1.697421e-04 1.151995e-03
## PC78 2.765648e-04 -3.878102e-04 9.409398e-04
## PC79 5.663015e-04 -1.042508e-04 1.236854e-03
## PC81 7.267212e-04 5.523200e-05 1.398210e-03
## PC82 4.337908e-04 -2.533935e-04 1.120975e-03
## PC83 -7.194573e-04 -1.403123e-03 -3.579173e-05
## PC84 7.996992e-04 1.137021e-04 1.485696e-03
## PC85 1.123558e-03 4.290312e-04 1.818084e-03
## PC87 1.719575e-03 1.029988e-03 2.409162e-03
## PC88 -1.139771e-03 -1.842020e-03 -4.375212e-04
## PC89 -5.395392e-04 -1.239624e-03 1.605451e-04
## PC90 -5.072518e-04 -1.208860e-03 1.943566e-04
## PC92 2.749095e-04 -4.208083e-04 9.706273e-04
## PC94 -9.179035e-04 -1.626069e-03 -2.097378e-04
## PC96 -4.613714e-04 -1.176317e-03 2.535744e-04
## PC97 -5.007501e-04 -1.211172e-03 2.096717e-04
## PC98 -4.817032e-04 -1.191269e-03 2.278624e-04
## PC99 -4.487862e-04 -1.159985e-03 2.624125e-04
## PC102 -5.760555e-04 -1.289414e-03 1.373025e-04
## PC104 -6.682706e-04 -1.388170e-03 5.162844e-05
## PC105 4.955110e-04 -2.268609e-04 1.217883e-03
## PC106 1.242436e-03 5.179929e-04 1.966879e-03
## PC107 6.103805e-04 -1.150509e-04 1.335812e-03
## PC109 5.375521e-04 -1.881497e-04 1.263254e-03
## PC110 -5.635217e-04 -1.293753e-03 1.667097e-04
## PC111 -8.082237e-04 -1.541821e-03 -7.462696e-05
## PC113 3.104138e-04 -4.253179e-04 1.046145e-03
## PC114 -7.563989e-04 -1.484119e-03 -2.867898e-05
## PC115 -1.655666e-03 -2.389151e-03 -9.221812e-04
## PC118 7.180344e-04 -2.119439e-05 1.457263e-03
## PC119 -5.373825e-04 -1.276933e-03 2.021678e-04
## PC121 -4.009325e-04 -1.143311e-03 3.414462e-04
## PC122 4.979362e-04 -2.400266e-04 1.235899e-03
## PC123 -5.413550e-04 -1.285929e-03 2.032187e-04
## PC125 4.774826e-04 -2.684608e-04 1.223426e-03
## PC128 -9.910001e-04 -1.736981e-03 -2.450190e-04
## PC130 4.081361e-04 -3.380762e-04 1.154348e-03
## PC131 -1.474609e-03 -2.219450e-03 -7.297668e-04
## PC132 3.074585e-04 -4.456296e-04 1.060547e-03
## PC134 9.756772e-04 2.242233e-04 1.727131e-03
## PC135 4.401274e-04 -3.112522e-04 1.191507e-03
## PC136 5.537986e-04 -2.028168e-04 1.310414e-03
## PC137 -7.524878e-04 -1.508038e-03 3.062572e-06
## PC138 5.529543e-04 -2.063313e-04 1.312240e-03
## PC139 -7.448016e-04 -1.499809e-03 1.020571e-05
## PC140 -3.901045e-04 -1.147415e-03 3.672062e-04
## PC141 3.924341e-04 -3.613440e-04 1.146212e-03
## PC143 3.158275e-04 -4.421895e-04 1.073844e-03
## PC144 1.024203e-03 2.633283e-04 1.785078e-03
## PC146 5.923295e-04 -1.751615e-04 1.359820e-03
## PC148 -5.130788e-04 -1.275746e-03 2.495885e-04
## PC151 6.756695e-04 -9.189504e-05 1.443234e-03
## PC152 -6.885784e-04 -1.455780e-03 7.862350e-05
## PC153 4.660142e-04 -3.072961e-04 1.239325e-03
## PC154 -8.514425e-04 -1.620867e-03 -8.201780e-05
## PC155 1.067769e-03 2.971624e-04 1.838375e-03
## PC156 1.368886e-03 5.966260e-04 2.141146e-03
## PC159 2.124070e-03 1.347256e-03 2.900884e-03
## PC161 3.374139e-04 -4.362380e-04 1.111066e-03
## PC162 -1.145268e-03 -1.925606e-03 -3.649295e-04
## PC163 6.712821e-04 -1.039883e-04 1.446553e-03
## PC164 3.014931e-04 -4.803026e-04 1.083289e-03Test
if (algo.forward.caret == TRUE){
test.model(model=model.forward, test=data.test
,method = 'leapForward',subopt = NULL
,formula = formula, feature.names = feature.names, label.names = label.names
,id = id
,draw.limits = TRUE, transformation = t)
}## [1] "Summary of predicted values: "
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 2.024 2.087 2.101 2.097 2.110 2.141
## [1] "leapForward Test MSE: 0.00102089613568136"
## [1] "leapForward Test RMSE: 0.0319514653135244"
## [1] "leapForward Test MSE (Org Scale): 90.4181132605647"
## [1] "leapForward Test RMSE (Org Scale): 9.50884394974304"
Backward Elimination with CV
Train
if (algo.backward.caret == TRUE){
set.seed(1)
returned = train.caret.glmselect(formula = formula
,data = data.train
,method = "leapBackward"
,feature.names = feature.names)
model.backward = returned$model
id = returned$id
}## Aggregating results
## Selecting tuning parameters
## Fitting nvmax = 110 on full training set
## [1] "All models results"
## nvmax RMSE Rsquared MAE RMSESD RsquaredSD MAESD
## 1 1 0.03477291 0.08867342 0.02692328 0.001241527 0.02694524 0.0007080957
## 2 2 0.03430526 0.11280445 0.02659499 0.001382164 0.03177241 0.0008448670
## 3 3 0.03397028 0.13012834 0.02629226 0.001480367 0.03628599 0.0009228758
## 4 4 0.03357202 0.15065682 0.02594497 0.001495727 0.03862072 0.0008898614
## 5 5 0.03329810 0.16453122 0.02572753 0.001417074 0.04025876 0.0008731997
## 6 6 0.03307787 0.17576857 0.02556677 0.001504730 0.04328083 0.0009446991
## 7 7 0.03306407 0.17615661 0.02557869 0.001452171 0.03968875 0.0009114778
## 8 8 0.03295739 0.18134530 0.02547827 0.001388292 0.03792930 0.0008274437
## 9 9 0.03287939 0.18540661 0.02543399 0.001348211 0.03725882 0.0008444702
## 10 10 0.03275470 0.19146665 0.02537654 0.001412011 0.03832877 0.0008875603
## 11 11 0.03263033 0.19759284 0.02525113 0.001364011 0.03659311 0.0008756810
## 12 12 0.03257233 0.20048903 0.02523311 0.001354071 0.03672316 0.0008542372
## 13 13 0.03251170 0.20352002 0.02521402 0.001350424 0.03679330 0.0008351289
## 14 14 0.03243637 0.20713813 0.02516582 0.001326182 0.03632042 0.0008198317
## 15 15 0.03236399 0.21078002 0.02508994 0.001340624 0.03820307 0.0008389046
## 16 16 0.03229713 0.21389724 0.02502812 0.001305601 0.03482762 0.0007953255
## 17 17 0.03220992 0.21809658 0.02496221 0.001315084 0.03542000 0.0007926923
## 18 18 0.03211348 0.22278477 0.02488082 0.001329096 0.03586858 0.0008024469
## 19 19 0.03212837 0.22212585 0.02490779 0.001341751 0.03746177 0.0008003150
## 20 20 0.03213781 0.22162102 0.02492734 0.001312032 0.03662545 0.0008052886
## 21 21 0.03213292 0.22181018 0.02493871 0.001309637 0.03648529 0.0008097871
## 22 22 0.03216415 0.22035170 0.02496546 0.001314688 0.03606900 0.0007887597
## 23 23 0.03218004 0.21978765 0.02499320 0.001345886 0.03797314 0.0008001592
## 24 24 0.03217962 0.21989948 0.02499754 0.001375751 0.03808737 0.0008155772
## 25 25 0.03214851 0.22141516 0.02496231 0.001390258 0.03864470 0.0008086626
## 26 26 0.03212614 0.22258862 0.02494025 0.001418549 0.03972298 0.0008370979
## 27 27 0.03210861 0.22350784 0.02493115 0.001397575 0.03933920 0.0008293077
## 28 28 0.03211566 0.22313668 0.02492613 0.001363803 0.03747320 0.0007978509
## 29 29 0.03213711 0.22235720 0.02493668 0.001391574 0.03860505 0.0008025450
## 30 30 0.03211669 0.22325500 0.02493446 0.001389989 0.03872350 0.0008086606
## 31 31 0.03207909 0.22488225 0.02492618 0.001376529 0.03929919 0.0008131397
## 32 32 0.03207245 0.22525612 0.02491403 0.001391883 0.04080784 0.0008220509
## 33 33 0.03205101 0.22624599 0.02491031 0.001414465 0.04119436 0.0008491636
## 34 34 0.03204038 0.22659548 0.02490480 0.001410639 0.03965959 0.0008407845
## 35 35 0.03205638 0.22595383 0.02491509 0.001421328 0.03969448 0.0008289471
## 36 36 0.03206960 0.22534588 0.02492428 0.001406537 0.03919583 0.0008087184
## 37 37 0.03205758 0.22583707 0.02492707 0.001397671 0.03917762 0.0008094775
## 38 38 0.03205322 0.22611470 0.02491297 0.001412162 0.03992544 0.0008194599
## 39 39 0.03204781 0.22642910 0.02489963 0.001412050 0.04036948 0.0008314135
## 40 40 0.03204261 0.22671345 0.02489137 0.001406340 0.04047229 0.0008341381
## 41 41 0.03204194 0.22681627 0.02489759 0.001388689 0.04040147 0.0008204343
## 42 42 0.03206928 0.22555906 0.02490955 0.001403987 0.04095464 0.0008232951
## 43 43 0.03206459 0.22584693 0.02490599 0.001421581 0.04094682 0.0008400139
## 44 44 0.03208054 0.22514515 0.02491116 0.001424649 0.04083853 0.0008497526
## 45 45 0.03210064 0.22431640 0.02492423 0.001435872 0.04100009 0.0008547758
## 46 46 0.03210628 0.22402150 0.02491449 0.001439508 0.04058852 0.0008573306
## 47 47 0.03209280 0.22471922 0.02491902 0.001432224 0.04059939 0.0008732838
## 48 48 0.03210532 0.22423489 0.02493032 0.001430459 0.04100737 0.0008879827
## 49 49 0.03211163 0.22404680 0.02493360 0.001434442 0.04132732 0.0008979772
## 50 50 0.03210694 0.22425560 0.02494084 0.001434283 0.04063111 0.0008854307
## 51 51 0.03211647 0.22386847 0.02494583 0.001417559 0.03972872 0.0008902399
## 52 52 0.03210766 0.22430848 0.02493085 0.001435295 0.03978106 0.0008894305
## 53 53 0.03213614 0.22308290 0.02495360 0.001421114 0.03948345 0.0008819039
## 54 54 0.03211956 0.22381943 0.02493168 0.001419330 0.03933501 0.0008807096
## 55 55 0.03212483 0.22349935 0.02494206 0.001407913 0.03907454 0.0008742864
## 56 56 0.03211216 0.22400631 0.02492988 0.001394593 0.03831464 0.0008699062
## 57 57 0.03211579 0.22398113 0.02494166 0.001413633 0.03940418 0.0008922376
## 58 58 0.03210192 0.22462028 0.02493502 0.001411151 0.03893947 0.0008804919
## 59 59 0.03213269 0.22331780 0.02495672 0.001422367 0.03917530 0.0008754991
## 60 60 0.03212672 0.22361511 0.02494886 0.001419111 0.03901162 0.0008757383
## 61 61 0.03211455 0.22429475 0.02493329 0.001449054 0.04001900 0.0008999164
## 62 62 0.03211156 0.22445435 0.02493655 0.001433003 0.03962380 0.0008864711
## 63 63 0.03210130 0.22495859 0.02494326 0.001431823 0.04007662 0.0008924303
## 64 64 0.03208969 0.22552763 0.02494012 0.001449938 0.04073208 0.0009102667
## 65 65 0.03207265 0.22631752 0.02492411 0.001445949 0.04051978 0.0009095516
## 66 66 0.03208134 0.22594272 0.02493487 0.001446019 0.04035424 0.0009152635
## 67 67 0.03208668 0.22581330 0.02493076 0.001467886 0.04168388 0.0009319928
## 68 68 0.03208124 0.22607877 0.02493223 0.001462110 0.04127941 0.0009433519
## 69 69 0.03207323 0.22648474 0.02491923 0.001472687 0.04156043 0.0009541251
## 70 70 0.03207017 0.22661973 0.02491569 0.001471120 0.04150434 0.0009530351
## 71 71 0.03207832 0.22630140 0.02492499 0.001464890 0.04120853 0.0009532068
## 72 72 0.03207177 0.22660594 0.02492913 0.001478852 0.04139493 0.0009545841
## 73 73 0.03208246 0.22610978 0.02493569 0.001469587 0.04032261 0.0009342418
## 74 74 0.03207333 0.22660173 0.02493100 0.001463948 0.04020081 0.0009359185
## 75 75 0.03206816 0.22688445 0.02492139 0.001472498 0.04059702 0.0009385040
## 76 76 0.03207009 0.22683524 0.02492349 0.001470099 0.04077888 0.0009345883
## 77 77 0.03206180 0.22727944 0.02491406 0.001478382 0.04097980 0.0009401027
## 78 78 0.03206461 0.22718097 0.02491839 0.001490932 0.04165749 0.0009645938
## 79 79 0.03206641 0.22712476 0.02491256 0.001496181 0.04177050 0.0009683861
## 80 80 0.03205529 0.22765676 0.02489975 0.001503489 0.04198825 0.0009836589
## 81 81 0.03204457 0.22811258 0.02489072 0.001500319 0.04184524 0.0009770287
## 82 82 0.03203653 0.22847008 0.02488121 0.001499180 0.04174717 0.0009735092
## 83 83 0.03202519 0.22896086 0.02487473 0.001515916 0.04228341 0.0009889464
## 84 84 0.03202412 0.22901156 0.02487772 0.001509442 0.04202499 0.0009777206
## 85 85 0.03201281 0.22945309 0.02487023 0.001499758 0.04157401 0.0009705243
## 86 86 0.03201595 0.22936249 0.02487838 0.001496303 0.04130307 0.0009805221
## 87 87 0.03200549 0.22984719 0.02486523 0.001495384 0.04121632 0.0009778452
## 88 88 0.03200260 0.23000738 0.02485790 0.001499264 0.04102508 0.0009852350
## 89 89 0.03198973 0.23058811 0.02485260 0.001496409 0.04044055 0.0009807616
## 90 90 0.03199463 0.23035628 0.02485844 0.001494202 0.04055486 0.0009777001
## 91 91 0.03199472 0.23032869 0.02485656 0.001490854 0.04014047 0.0009707329
## 92 92 0.03199470 0.23037548 0.02486261 0.001494151 0.04023059 0.0009690020
## 93 93 0.03200044 0.23012470 0.02487000 0.001495062 0.03987310 0.0009753613
## 94 94 0.03200030 0.23009599 0.02487314 0.001487746 0.03968025 0.0009761965
## 95 95 0.03199030 0.23060098 0.02486373 0.001500013 0.04007995 0.0009896515
## 96 96 0.03199764 0.23031777 0.02486092 0.001503197 0.04010516 0.0009930310
## 97 97 0.03199814 0.23028712 0.02485950 0.001519767 0.04058028 0.0009996734
## 98 98 0.03199203 0.23054318 0.02485312 0.001524204 0.04048117 0.0009986949
## 99 99 0.03199760 0.23030316 0.02485463 0.001532446 0.04055220 0.0010063278
## 100 100 0.03199562 0.23039090 0.02485536 0.001528618 0.04052124 0.0010069527
## 101 101 0.03199256 0.23051327 0.02485819 0.001521955 0.03993837 0.0009966870
## 102 102 0.03199172 0.23056819 0.02485462 0.001524524 0.04016561 0.0009981462
## 103 103 0.03197871 0.23114909 0.02484476 0.001525203 0.04043456 0.0009987292
## 104 104 0.03197442 0.23134640 0.02484161 0.001529584 0.04039329 0.0010055524
## 105 105 0.03197723 0.23123436 0.02483659 0.001532022 0.04045956 0.0010119291
## 106 106 0.03197358 0.23140859 0.02483619 0.001533794 0.04089880 0.0010164772
## 107 107 0.03197305 0.23144303 0.02483680 0.001539769 0.04097211 0.0010192725
## 108 108 0.03197343 0.23144234 0.02483566 0.001547970 0.04135446 0.0010292884
## 109 109 0.03197504 0.23134488 0.02483593 0.001545829 0.04117435 0.0010236430
## 110 110 0.03197190 0.23146242 0.02482630 0.001536594 0.04082764 0.0010154066
## 111 111 0.03197442 0.23135094 0.02482692 0.001535600 0.04110020 0.0010127780
## 112 112 0.03197246 0.23149132 0.02482195 0.001536747 0.04117865 0.0010072769
## 113 113 0.03197461 0.23137605 0.02482809 0.001531756 0.04104360 0.0010053112
## 114 114 0.03197604 0.23132361 0.02482609 0.001528680 0.04094427 0.0010053142
## 115 115 0.03197837 0.23122685 0.02483174 0.001530312 0.04067612 0.0010056174
## 116 116 0.03197979 0.23118245 0.02483204 0.001530900 0.04075648 0.0010049239
## 117 117 0.03198423 0.23099071 0.02483741 0.001524602 0.04059462 0.0010025404
## 118 118 0.03198748 0.23086744 0.02484001 0.001524930 0.04057813 0.0009998928
## 119 119 0.03199519 0.23053784 0.02484830 0.001525864 0.04054937 0.0010003865
## 120 120 0.03198976 0.23078268 0.02484224 0.001526166 0.04039139 0.0010019231
## 121 121 0.03198885 0.23082304 0.02484123 0.001523881 0.04011096 0.0009993482
## 122 122 0.03199615 0.23052753 0.02484857 0.001524203 0.04019993 0.0009978955
## 123 123 0.03199822 0.23042646 0.02484948 0.001520157 0.04005783 0.0009911628
## 124 124 0.03200088 0.23032480 0.02485123 0.001522284 0.04027961 0.0009901903
## 125 125 0.03199964 0.23036807 0.02484816 0.001522779 0.04032824 0.0009907574
## 126 126 0.03200003 0.23038047 0.02484480 0.001523229 0.04039877 0.0009974876
## 127 127 0.03200552 0.23015056 0.02484835 0.001524890 0.04057208 0.0009998711
## 128 128 0.03200849 0.23002288 0.02485181 0.001528606 0.04074557 0.0010019670
## 129 129 0.03200626 0.23011574 0.02484972 0.001527317 0.04070563 0.0010032649
## 130 130 0.03200723 0.23010004 0.02485102 0.001527097 0.04074447 0.0010069934
## 131 131 0.03201137 0.22992104 0.02485348 0.001528458 0.04078396 0.0010063671
## 132 132 0.03200983 0.22999040 0.02485419 0.001530295 0.04084604 0.0010071048
## 133 133 0.03201344 0.22984440 0.02485941 0.001533387 0.04108508 0.0010103116
## 134 134 0.03201365 0.22984281 0.02486109 0.001534540 0.04101024 0.0010112674
## 135 135 0.03201087 0.22997089 0.02485950 0.001532274 0.04101278 0.0010095930
## 136 136 0.03200837 0.23008806 0.02485724 0.001532864 0.04107810 0.0010121125
## 137 137 0.03200963 0.23002545 0.02485927 0.001531753 0.04099892 0.0010112603
## 138 138 0.03201521 0.22978175 0.02486343 0.001529153 0.04079978 0.0010098656
## 139 139 0.03201480 0.22979429 0.02486421 0.001529846 0.04086330 0.0010113660
## 140 140 0.03201422 0.22981594 0.02486244 0.001528604 0.04084881 0.0010119257
## 141 141 0.03201762 0.22966093 0.02486391 0.001527853 0.04080573 0.0010124458
## 142 142 0.03201652 0.22972501 0.02486216 0.001529424 0.04087584 0.0010118080
## 143 143 0.03201593 0.22975229 0.02486209 0.001532447 0.04099954 0.0010146881
## 144 144 0.03201685 0.22972231 0.02486141 0.001533976 0.04103142 0.0010153620
## 145 145 0.03201745 0.22970677 0.02486172 0.001533723 0.04103160 0.0010156287
## 146 146 0.03201830 0.22966711 0.02486291 0.001532618 0.04100083 0.0010146294
## 147 147 0.03201959 0.22961148 0.02486442 0.001533643 0.04103777 0.0010153806
## 148 148 0.03202083 0.22956075 0.02486592 0.001532662 0.04098088 0.0010129589
## 149 149 0.03202186 0.22952486 0.02486700 0.001534175 0.04101414 0.0010138945
## 150 150 0.03202152 0.22954559 0.02486707 0.001536138 0.04108821 0.0010166699
## 151 151 0.03202283 0.22948672 0.02486717 0.001536222 0.04104770 0.0010162828
## 152 152 0.03202294 0.22948434 0.02486700 0.001536319 0.04107400 0.0010171523
## 153 153 0.03202280 0.22949054 0.02486656 0.001536304 0.04106531 0.0010170736
## 154 154 0.03202125 0.22955754 0.02486463 0.001536783 0.04108383 0.0010179749
## 155 155 0.03202162 0.22953372 0.02486414 0.001537131 0.04110253 0.0010177444
## 156 156 0.03202231 0.22950264 0.02486497 0.001537206 0.04114068 0.0010179990
## 157 157 0.03202253 0.22949211 0.02486553 0.001535889 0.04110959 0.0010174766
## 158 158 0.03202272 0.22948379 0.02486528 0.001536237 0.04110658 0.0010176311
## 159 159 0.03202318 0.22946528 0.02486570 0.001535923 0.04109475 0.0010176663
## 160 160 0.03202287 0.22948068 0.02486567 0.001536339 0.04111202 0.0010178004
## 161 161 0.03202274 0.22948616 0.02486571 0.001536346 0.04111327 0.0010175342
## 162 162 0.03202292 0.22947816 0.02486583 0.001536473 0.04111787 0.0010178911
## 163 163 0.03202284 0.22948087 0.02486558 0.001536518 0.04112019 0.0010179683
## 164 164 0.03202267 0.22948948 0.02486541 0.001536708 0.04113085 0.0010181546
## [1] "Best Model"
## nvmax
## 110 110
## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
## [1] "Coefficients of final model:"
## Estimate 2.5 % 97.5 %
## (Intercept) 2.096921e+00 2.096096e+00 2.097746e+00
## PC1 -4.820829e-04 -5.540102e-04 -4.101556e-04
## PC2 -9.439758e-04 -1.017022e-03 -8.709292e-04
## PC3 -4.376253e-04 -5.110635e-04 -3.641872e-04
## PC4 -3.485515e-04 -4.229921e-04 -2.741108e-04
## PC5 2.305793e-04 1.538579e-04 3.073007e-04
## PC6 -9.916849e-05 -1.759127e-04 -2.242430e-05
## PC7 -2.034675e-04 -2.818330e-04 -1.251020e-04
## PC8 -3.732177e-05 -1.175225e-04 4.287892e-05
## PC9 -5.229907e-05 -1.344202e-04 2.982208e-05
## PC11 -5.388938e-04 -6.279221e-04 -4.498656e-04
## PC12 -5.049829e-04 -5.988052e-04 -4.111606e-04
## PC13 3.431100e-04 2.475465e-04 4.386736e-04
## PC14 2.527666e-04 1.537902e-04 3.517430e-04
## PC16 3.558417e-04 2.538653e-04 4.578182e-04
## PC17 -1.998529e-04 -3.074757e-04 -9.223015e-05
## PC18 -3.654310e-04 -4.773739e-04 -2.534881e-04
## PC19 4.317135e-05 -7.010991e-05 1.564526e-04
## PC20 4.101492e-04 2.862502e-04 5.340482e-04
## PC21 8.180626e-05 -4.747785e-05 2.110904e-04
## PC22 9.282618e-05 -1.090969e-04 2.947493e-04
## PC23 2.053985e-04 -4.390229e-05 4.546993e-04
## PC24 -7.967536e-04 -1.087088e-03 -5.064190e-04
## PC25 2.524151e-04 -7.599813e-05 5.808283e-04
## PC26 3.833125e-04 4.667886e-05 7.199461e-04
## PC27 2.715470e-04 -6.361989e-05 6.067139e-04
## PC29 3.679176e-04 -5.941506e-06 7.417766e-04
## PC32 -7.123956e-04 -1.128028e-03 -2.967633e-04
## PC33 7.039065e-04 2.795701e-04 1.128243e-03
## PC34 1.099756e-03 6.511037e-04 1.548408e-03
## PC37 -3.603607e-04 -8.610729e-04 1.403515e-04
## PC38 2.032648e-04 -3.141561e-04 7.206857e-04
## PC39 -2.080906e-04 -7.413170e-04 3.251358e-04
## PC42 -2.251949e-04 -7.889242e-04 3.385343e-04
## PC44 6.421781e-04 7.553640e-05 1.208820e-03
## PC45 -2.968457e-04 -8.659781e-04 2.722868e-04
## PC47 -4.846403e-04 -1.054791e-03 8.551069e-05
## PC49 3.431287e-04 -2.384184e-04 9.246758e-04
## PC57 -7.572567e-04 -1.370314e-03 -1.441993e-04
## PC59 9.818223e-04 3.716729e-04 1.591972e-03
## PC62 -3.745738e-04 -1.004500e-03 2.553524e-04
## PC63 -7.029549e-04 -1.328927e-03 -7.698276e-05
## PC64 -9.023538e-04 -1.535550e-03 -2.691578e-04
## PC66 -4.331374e-04 -1.073173e-03 2.068977e-04
## PC68 4.950411e-04 -1.474936e-04 1.137576e-03
## PC71 5.213597e-04 -1.282802e-04 1.171000e-03
## PC73 4.679612e-04 -1.857211e-04 1.121643e-03
## PC74 -6.580551e-04 -1.315861e-03 -2.495721e-07
## PC75 -8.829193e-04 -1.546441e-03 -2.193976e-04
## PC77 4.911264e-04 -1.697421e-04 1.151995e-03
## PC78 2.765648e-04 -3.878102e-04 9.409398e-04
## PC79 5.663015e-04 -1.042508e-04 1.236854e-03
## PC81 7.267212e-04 5.523200e-05 1.398210e-03
## PC82 4.337908e-04 -2.533935e-04 1.120975e-03
## PC83 -7.194573e-04 -1.403123e-03 -3.579173e-05
## PC84 7.996992e-04 1.137021e-04 1.485696e-03
## PC85 1.123558e-03 4.290312e-04 1.818084e-03
## PC87 1.719575e-03 1.029988e-03 2.409162e-03
## PC88 -1.139771e-03 -1.842020e-03 -4.375212e-04
## PC89 -5.395392e-04 -1.239624e-03 1.605451e-04
## PC90 -5.072518e-04 -1.208860e-03 1.943566e-04
## PC92 2.749095e-04 -4.208083e-04 9.706273e-04
## PC94 -9.179035e-04 -1.626069e-03 -2.097378e-04
## PC96 -4.613714e-04 -1.176317e-03 2.535744e-04
## PC97 -5.007501e-04 -1.211172e-03 2.096717e-04
## PC98 -4.817032e-04 -1.191269e-03 2.278624e-04
## PC99 -4.487862e-04 -1.159985e-03 2.624125e-04
## PC102 -5.760555e-04 -1.289414e-03 1.373025e-04
## PC104 -6.682706e-04 -1.388170e-03 5.162844e-05
## PC105 4.955110e-04 -2.268609e-04 1.217883e-03
## PC106 1.242436e-03 5.179929e-04 1.966879e-03
## PC107 6.103805e-04 -1.150509e-04 1.335812e-03
## PC109 5.375521e-04 -1.881497e-04 1.263254e-03
## PC110 -5.635217e-04 -1.293753e-03 1.667097e-04
## PC111 -8.082237e-04 -1.541821e-03 -7.462696e-05
## PC113 3.104138e-04 -4.253179e-04 1.046145e-03
## PC114 -7.563989e-04 -1.484119e-03 -2.867898e-05
## PC115 -1.655666e-03 -2.389151e-03 -9.221812e-04
## PC118 7.180344e-04 -2.119439e-05 1.457263e-03
## PC119 -5.373825e-04 -1.276933e-03 2.021678e-04
## PC121 -4.009325e-04 -1.143311e-03 3.414462e-04
## PC122 4.979362e-04 -2.400266e-04 1.235899e-03
## PC123 -5.413550e-04 -1.285929e-03 2.032187e-04
## PC125 4.774826e-04 -2.684608e-04 1.223426e-03
## PC128 -9.910001e-04 -1.736981e-03 -2.450190e-04
## PC130 4.081361e-04 -3.380762e-04 1.154348e-03
## PC131 -1.474609e-03 -2.219450e-03 -7.297668e-04
## PC132 3.074585e-04 -4.456296e-04 1.060547e-03
## PC134 9.756772e-04 2.242233e-04 1.727131e-03
## PC135 4.401274e-04 -3.112522e-04 1.191507e-03
## PC136 5.537986e-04 -2.028168e-04 1.310414e-03
## PC137 -7.524878e-04 -1.508038e-03 3.062572e-06
## PC138 5.529543e-04 -2.063313e-04 1.312240e-03
## PC139 -7.448016e-04 -1.499809e-03 1.020571e-05
## PC140 -3.901045e-04 -1.147415e-03 3.672062e-04
## PC141 3.924341e-04 -3.613440e-04 1.146212e-03
## PC143 3.158275e-04 -4.421895e-04 1.073844e-03
## PC144 1.024203e-03 2.633283e-04 1.785078e-03
## PC146 5.923295e-04 -1.751615e-04 1.359820e-03
## PC148 -5.130788e-04 -1.275746e-03 2.495885e-04
## PC151 6.756695e-04 -9.189504e-05 1.443234e-03
## PC152 -6.885784e-04 -1.455780e-03 7.862350e-05
## PC153 4.660142e-04 -3.072961e-04 1.239325e-03
## PC154 -8.514425e-04 -1.620867e-03 -8.201780e-05
## PC155 1.067769e-03 2.971624e-04 1.838375e-03
## PC156 1.368886e-03 5.966260e-04 2.141146e-03
## PC159 2.124070e-03 1.347256e-03 2.900884e-03
## PC161 3.374139e-04 -4.362380e-04 1.111066e-03
## PC162 -1.145268e-03 -1.925606e-03 -3.649295e-04
## PC163 6.712821e-04 -1.039883e-04 1.446553e-03
## PC164 3.014931e-04 -4.803026e-04 1.083289e-03Test
if (algo.backward.caret == TRUE){
test.model(model.backward, data.test
,method = 'leapBackward',subopt = NULL
,formula = formula, feature.names = feature.names, label.names = label.names
,id = id
,draw.limits = TRUE, transformation = t)
}## [1] "Summary of predicted values: "
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 2.024 2.087 2.101 2.097 2.110 2.141
## [1] "leapBackward Test MSE: 0.00102089613568136"
## [1] "leapBackward Test RMSE: 0.0319514653135244"
## [1] "leapBackward Test MSE (Org Scale): 90.4181132605647"
## [1] "leapBackward Test RMSE (Org Scale): 9.50884394974304"
Stepwise Selection with CV
Train
if (algo.stepwise.caret == TRUE){
set.seed(1)
returned = train.caret.glmselect(formula = formula
,data = data.train
,method = "leapSeq"
,feature.names = feature.names)
model.stepwise = returned$model
id = returned$id
}## Aggregating results
## Selecting tuning parameters
## Fitting nvmax = 110 on full training set
## [1] "All models results"
## nvmax RMSE Rsquared MAE RMSESD RsquaredSD MAESD
## 1 1 0.03477291 0.08867342 0.02692328 0.001241527 0.02694524 0.0007080957
## 2 2 0.03430526 0.11280445 0.02659499 0.001382164 0.03177241 0.0008448670
## 3 3 0.03397028 0.13012834 0.02629226 0.001480367 0.03628599 0.0009228758
## 4 4 0.03368539 0.14538925 0.02606470 0.001501094 0.03730811 0.0009134034
## 5 5 0.03329810 0.16453122 0.02572753 0.001417074 0.04025876 0.0008731997
## 6 6 0.03364346 0.14762605 0.02606217 0.001507226 0.03744262 0.0009118042
## 7 7 0.03306407 0.17615661 0.02557869 0.001452171 0.03968875 0.0009114778
## 8 8 0.03295739 0.18134530 0.02547827 0.001388292 0.03792930 0.0008274437
## 9 9 0.03294086 0.18231882 0.02548121 0.001348559 0.03811940 0.0008221184
## 10 10 0.03295196 0.18193795 0.02554625 0.001782672 0.05165982 0.0011296783
## 11 11 0.03278176 0.19005293 0.02536550 0.001226074 0.03662664 0.0007614728
## 12 12 0.03262333 0.19832480 0.02528612 0.001354081 0.03543918 0.0008453433
## 13 13 0.03249855 0.20394578 0.02517899 0.001340311 0.03643932 0.0007938316
## 14 14 0.03244689 0.20662371 0.02517335 0.001343122 0.03644511 0.0008246527
## 15 15 0.03237508 0.21024129 0.02509782 0.001358417 0.03834147 0.0008435020
## 16 16 0.03229713 0.21389724 0.02502812 0.001305601 0.03482762 0.0007953255
## 17 17 0.03228024 0.21477143 0.02501865 0.001441694 0.03767126 0.0008421591
## 18 18 0.03211348 0.22278477 0.02488082 0.001329096 0.03586858 0.0008024469
## 19 19 0.03212837 0.22212585 0.02490779 0.001341751 0.03746177 0.0008003150
## 20 20 0.03213781 0.22162102 0.02492734 0.001312032 0.03662545 0.0008052886
## 21 21 0.03213292 0.22181018 0.02493871 0.001309637 0.03648529 0.0008097871
## 22 22 0.03216415 0.22035170 0.02496546 0.001314688 0.03606900 0.0007887597
## 23 23 0.03223054 0.21740961 0.02503639 0.001432144 0.03921016 0.0008294727
## 24 24 0.03221847 0.21802288 0.02499991 0.001404291 0.03862676 0.0008177595
## 25 25 0.03216149 0.22080358 0.02497778 0.001375812 0.03724828 0.0008036009
## 26 26 0.03212614 0.22258862 0.02494025 0.001418549 0.03972298 0.0008370979
## 27 27 0.03214944 0.22158627 0.02494780 0.001458076 0.04017474 0.0008355988
## 28 28 0.03211566 0.22313668 0.02492613 0.001363803 0.03747320 0.0007978509
## 29 29 0.03218994 0.21951031 0.02493448 0.001436620 0.04157301 0.0008278866
## 30 30 0.03211594 0.22319337 0.02493399 0.001400114 0.04048388 0.0008208170
## 31 31 0.03207909 0.22488225 0.02492618 0.001376529 0.03929919 0.0008131397
## 32 32 0.03206701 0.22507278 0.02491505 0.001393636 0.04100214 0.0008220187
## 33 33 0.03207480 0.22505448 0.02490972 0.001405358 0.04126198 0.0008488342
## 34 34 0.03204038 0.22659548 0.02490480 0.001410639 0.03965959 0.0008407845
## 35 35 0.03203920 0.22676001 0.02490051 0.001440626 0.04120706 0.0008483916
## 36 36 0.03205493 0.22605123 0.02491630 0.001428149 0.04018208 0.0008259982
## 37 37 0.03209247 0.22448256 0.02493880 0.001373083 0.03699118 0.0007959057
## 38 38 0.03209946 0.22392211 0.02493283 0.001392169 0.03975165 0.0008295505
## 39 39 0.03206745 0.22560525 0.02490482 0.001384284 0.03932639 0.0008207336
## 40 40 0.03212107 0.22320888 0.02490222 0.001374020 0.03771811 0.0007961591
## 41 41 0.03204194 0.22681627 0.02489759 0.001388689 0.04040147 0.0008204343
## 42 42 0.03206928 0.22555906 0.02490955 0.001403987 0.04095464 0.0008232951
## 43 43 0.03206459 0.22584693 0.02490599 0.001421581 0.04094682 0.0008400139
## 44 44 0.03208054 0.22514515 0.02491116 0.001424649 0.04083853 0.0008497526
## 45 45 0.03209622 0.22450274 0.02491986 0.001435414 0.04092379 0.0008529708
## 46 46 0.03210495 0.22363884 0.02490932 0.001442367 0.04129948 0.0008447148
## 47 47 0.03210457 0.22416884 0.02496012 0.001435905 0.04059665 0.0008571557
## 48 48 0.03215396 0.22208390 0.02496497 0.001367959 0.03540737 0.0008392124
## 49 49 0.03211062 0.22404659 0.02493303 0.001433535 0.04132750 0.0008970393
## 50 50 0.03209726 0.22436420 0.02494961 0.001416106 0.04016010 0.0008928591
## 51 51 0.03211101 0.22405961 0.02494186 0.001412430 0.03954804 0.0008834049
## 52 52 0.03217387 0.22061515 0.02498129 0.001391007 0.04071029 0.0008897043
## 53 53 0.03218264 0.22077620 0.02494981 0.001429008 0.04076332 0.0008810413
## 54 54 0.03216400 0.22198101 0.02497226 0.001382859 0.03559469 0.0008410044
## 55 55 0.03212483 0.22349935 0.02494206 0.001407913 0.03907454 0.0008742864
## 56 56 0.03211988 0.22366659 0.02493888 0.001390261 0.03823314 0.0008750261
## 57 57 0.03211959 0.22379649 0.02495186 0.001411565 0.03936397 0.0008980209
## 58 58 0.03211239 0.22416596 0.02494613 0.001415538 0.03898629 0.0008897171
## 59 59 0.03212545 0.22365908 0.02495682 0.001432631 0.03946297 0.0008790120
## 60 60 0.03212316 0.22378696 0.02494761 0.001412651 0.03888734 0.0008747153
## 61 61 0.03213229 0.22284483 0.02493115 0.001428787 0.04044992 0.0008843802
## 62 62 0.03211137 0.22419724 0.02493487 0.001442324 0.03994127 0.0008862970
## 63 63 0.03210130 0.22495859 0.02494326 0.001431823 0.04007662 0.0008924303
## 64 64 0.03212862 0.22353731 0.02493078 0.001454168 0.04170003 0.0009058972
## 65 65 0.03207369 0.22624304 0.02492354 0.001446947 0.04059217 0.0009086123
## 66 66 0.03208122 0.22592667 0.02492976 0.001445905 0.04036995 0.0009069383
## 67 67 0.03208651 0.22577119 0.02492386 0.001467726 0.04172392 0.0009210062
## 68 68 0.03208446 0.22595476 0.02492810 0.001461677 0.04126619 0.0009395816
## 69 69 0.03205910 0.22649728 0.02489462 0.001448053 0.04099376 0.0009063671
## 70 70 0.03207017 0.22661973 0.02491569 0.001471120 0.04150434 0.0009530351
## 71 71 0.03212585 0.22402256 0.02497390 0.001434907 0.03861433 0.0009287974
## 72 72 0.03207177 0.22660594 0.02492913 0.001478852 0.04139493 0.0009545841
## 73 73 0.03207884 0.22627552 0.02493485 0.001469068 0.04036586 0.0009346723
## 74 74 0.03207339 0.22659491 0.02493149 0.001463956 0.04019921 0.0009356794
## 75 75 0.03206740 0.22692688 0.02491881 0.001474248 0.04055087 0.0009335688
## 76 76 0.03209832 0.22548493 0.02495169 0.001476863 0.04066274 0.0009247455
## 77 77 0.03206180 0.22727944 0.02491406 0.001478382 0.04097980 0.0009401027
## 78 78 0.03210466 0.22514188 0.02491065 0.001492263 0.04234991 0.0009652147
## 79 79 0.03206641 0.22712476 0.02491256 0.001496181 0.04177050 0.0009683861
## 80 80 0.03213538 0.22331485 0.02494660 0.001497440 0.04525489 0.0009907187
## 81 81 0.03205316 0.22773533 0.02489855 0.001505466 0.04189693 0.0009817560
## 82 82 0.03204522 0.22810910 0.02489000 0.001515063 0.04205617 0.0009825367
## 83 83 0.03209940 0.22557559 0.02491597 0.001483113 0.04203845 0.0010088293
## 84 84 0.03205112 0.22794690 0.02488631 0.001492402 0.04020826 0.0009679658
## 85 85 0.03201806 0.22884793 0.02488286 0.001507537 0.04221983 0.0009846185
## 86 86 0.03202085 0.22917024 0.02487680 0.001505395 0.04147502 0.0009788390
## 87 87 0.03203653 0.22846550 0.02489505 0.001515744 0.04140317 0.0009708080
## 88 88 0.03200244 0.22999129 0.02485773 0.001499302 0.04104252 0.0009852717
## 89 89 0.03203843 0.22804545 0.02484371 0.001458541 0.04024568 0.0009581253
## 90 90 0.03202266 0.22898510 0.02487562 0.001450038 0.03835310 0.0009338068
## 91 91 0.03199410 0.23035360 0.02485436 0.001491790 0.04017857 0.0009754344
## 92 92 0.03199145 0.23051231 0.02485813 0.001501909 0.04064253 0.0009808718
## 93 93 0.03209082 0.22576404 0.02494425 0.001429129 0.03971036 0.0009815257
## 94 94 0.03198553 0.23027567 0.02485954 0.001473212 0.03947547 0.0009532572
## 95 95 0.03202998 0.22870485 0.02489114 0.001444778 0.03757072 0.0009341900
## 96 96 0.03199788 0.23041260 0.02485618 0.001503094 0.04026775 0.0009965283
## 97 97 0.03199814 0.23028712 0.02485950 0.001519767 0.04058028 0.0009996734
## 98 98 0.03205836 0.22734122 0.02492342 0.001465661 0.04025952 0.0009868548
## 99 99 0.03199502 0.23042438 0.02485221 0.001532208 0.04059236 0.0010076699
## 100 100 0.03203984 0.22819130 0.02486701 0.001533326 0.04152059 0.0010087978
## 101 101 0.03199256 0.23051327 0.02485819 0.001521955 0.03993837 0.0009966870
## 102 102 0.03199608 0.22989097 0.02487171 0.001511168 0.03959427 0.0009545563
## 103 103 0.03197542 0.23140292 0.02483410 0.001527545 0.04088315 0.0010061924
## 104 104 0.03197442 0.23134640 0.02484161 0.001529584 0.04039329 0.0010055524
## 105 105 0.03197723 0.23123436 0.02483659 0.001532022 0.04045956 0.0010119291
## 106 106 0.03197358 0.23140859 0.02483619 0.001533794 0.04089880 0.0010164772
## 107 107 0.03198969 0.23029103 0.02486281 0.001535890 0.04228560 0.0010146620
## 108 108 0.03197029 0.23154870 0.02483612 0.001541826 0.04123377 0.0010298468
## 109 109 0.03197142 0.23147689 0.02483488 0.001538675 0.04102166 0.0010223219
## 110 110 0.03196823 0.23159643 0.02482476 0.001529341 0.04067338 0.0010134655
## 111 111 0.03197336 0.23138431 0.02482805 0.001533506 0.04106195 0.0010142136
## 112 112 0.03197246 0.23149132 0.02482195 0.001536747 0.04117865 0.0010072769
## 113 113 0.03197274 0.23125381 0.02480490 0.001528061 0.04118519 0.0009785909
## 114 114 0.03197604 0.23132361 0.02482609 0.001528680 0.04094427 0.0010053142
## 115 115 0.03197837 0.23122685 0.02483174 0.001530312 0.04067612 0.0010056174
## 116 116 0.03197979 0.23118245 0.02483204 0.001530900 0.04075648 0.0010049239
## 117 117 0.03198423 0.23099071 0.02483741 0.001524602 0.04059462 0.0010025404
## 118 118 0.03198748 0.23086744 0.02484001 0.001524930 0.04057813 0.0009998928
## 119 119 0.03199519 0.23053784 0.02484830 0.001525864 0.04054937 0.0010003865
## 120 120 0.03197408 0.23124329 0.02480665 0.001495980 0.03990187 0.0009640899
## 121 121 0.03198885 0.23082304 0.02484123 0.001523881 0.04011096 0.0009993482
## 122 122 0.03199615 0.23052753 0.02484857 0.001524203 0.04019993 0.0009978955
## 123 123 0.03199822 0.23042646 0.02484948 0.001520157 0.04005783 0.0009911628
## 124 124 0.03200088 0.23032480 0.02485123 0.001522284 0.04027961 0.0009901903
## 125 125 0.03200034 0.23011680 0.02483202 0.001523590 0.04056994 0.0009803431
## 126 126 0.03200152 0.23009132 0.02482920 0.001524954 0.04067482 0.0009875120
## 127 127 0.03198818 0.23049727 0.02483545 0.001506655 0.04014355 0.0009768843
## 128 128 0.03200849 0.23002288 0.02485181 0.001528606 0.04074557 0.0010019670
## 129 129 0.03200626 0.23011574 0.02484972 0.001527317 0.04070563 0.0010032649
## 130 130 0.03200723 0.23010004 0.02485102 0.001527097 0.04074447 0.0010069934
## 131 131 0.03200245 0.23012813 0.02483505 0.001518456 0.04059960 0.0009949585
## 132 132 0.03200983 0.22999040 0.02485419 0.001530295 0.04084604 0.0010071048
## 133 133 0.03201344 0.22984440 0.02485941 0.001533387 0.04108508 0.0010103116
## 134 134 0.03201365 0.22984281 0.02486109 0.001534540 0.04101024 0.0010112674
## 135 135 0.03201087 0.22997089 0.02485950 0.001532274 0.04101278 0.0010095930
## 136 136 0.03200837 0.23008806 0.02485724 0.001532864 0.04107810 0.0010121125
## 137 137 0.03200963 0.23002545 0.02485927 0.001531753 0.04099892 0.0010112603
## 138 138 0.03201521 0.22978175 0.02486343 0.001529153 0.04079978 0.0010098656
## 139 139 0.03201903 0.22916043 0.02487057 0.001480527 0.03967488 0.0009688835
## 140 140 0.03201422 0.22981594 0.02486244 0.001528604 0.04084881 0.0010119257
## 141 141 0.03200274 0.23002420 0.02484646 0.001512081 0.04035938 0.0009811341
## 142 142 0.03200153 0.23021949 0.02484716 0.001512919 0.04045506 0.0010025637
## 143 143 0.03201593 0.22975229 0.02486209 0.001532447 0.04099954 0.0010146881
## 144 144 0.03203446 0.22884630 0.02487070 0.001507502 0.03968331 0.0009960091
## 145 145 0.03201745 0.22970677 0.02486172 0.001533723 0.04103160 0.0010156287
## 146 146 0.03204051 0.22858179 0.02488113 0.001533606 0.04136434 0.0010181282
## 147 147 0.03201959 0.22961148 0.02486442 0.001533643 0.04103777 0.0010153806
## 148 148 0.03203008 0.22909522 0.02487562 0.001521796 0.04074210 0.0010074981
## 149 149 0.03203274 0.22898076 0.02487742 0.001521453 0.04074008 0.0010080632
## 150 150 0.03202152 0.22954559 0.02486707 0.001536138 0.04108821 0.0010166699
## 151 151 0.03202283 0.22948672 0.02486717 0.001536222 0.04104770 0.0010162828
## 152 152 0.03202515 0.22937927 0.02487262 0.001536550 0.04104296 0.0010142180
## 153 153 0.03202280 0.22949054 0.02486656 0.001536304 0.04106531 0.0010170736
## 154 154 0.03202125 0.22955754 0.02486463 0.001536783 0.04108383 0.0010179749
## 155 155 0.03202162 0.22953372 0.02486414 0.001537131 0.04110253 0.0010177444
## 156 156 0.03202231 0.22950264 0.02486497 0.001537206 0.04114068 0.0010179990
## 157 157 0.03203734 0.22880799 0.02488339 0.001533359 0.04192871 0.0010152820
## 158 158 0.03203789 0.22878322 0.02488330 0.001533634 0.04194449 0.0010153819
## 159 159 0.03202387 0.22941793 0.02486642 0.001536021 0.04112788 0.0010202464
## 160 160 0.03201321 0.22976841 0.02486820 0.001524236 0.04057383 0.0010087807
## 161 161 0.03202871 0.22918760 0.02487485 0.001529922 0.04087070 0.0010117449
## 162 162 0.03201966 0.22958734 0.02486870 0.001534560 0.04116043 0.0010113049
## 163 163 0.03201627 0.22978243 0.02486023 0.001539102 0.04121090 0.0010182024
## 164 164 0.03202267 0.22948948 0.02486541 0.001536708 0.04113085 0.0010181546
## [1] "Best Model"
## nvmax
## 110 110
## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
## [1] "Coefficients of final model:"
## Estimate 2.5 % 97.5 %
## (Intercept) 2.096921e+00 2.096096e+00 2.097746e+00
## PC1 -4.820829e-04 -5.540102e-04 -4.101556e-04
## PC2 -9.439758e-04 -1.017022e-03 -8.709292e-04
## PC3 -4.376253e-04 -5.110635e-04 -3.641872e-04
## PC4 -3.485515e-04 -4.229921e-04 -2.741108e-04
## PC5 2.305793e-04 1.538579e-04 3.073007e-04
## PC6 -9.916849e-05 -1.759127e-04 -2.242430e-05
## PC7 -2.034675e-04 -2.818330e-04 -1.251020e-04
## PC8 -3.732177e-05 -1.175225e-04 4.287892e-05
## PC9 -5.229907e-05 -1.344202e-04 2.982208e-05
## PC11 -5.388938e-04 -6.279221e-04 -4.498656e-04
## PC12 -5.049829e-04 -5.988052e-04 -4.111606e-04
## PC13 3.431100e-04 2.475465e-04 4.386736e-04
## PC14 2.527666e-04 1.537902e-04 3.517430e-04
## PC16 3.558417e-04 2.538653e-04 4.578182e-04
## PC17 -1.998529e-04 -3.074757e-04 -9.223015e-05
## PC18 -3.654310e-04 -4.773739e-04 -2.534881e-04
## PC19 4.317135e-05 -7.010991e-05 1.564526e-04
## PC20 4.101492e-04 2.862502e-04 5.340482e-04
## PC21 8.180626e-05 -4.747785e-05 2.110904e-04
## PC22 9.282618e-05 -1.090969e-04 2.947493e-04
## PC23 2.053985e-04 -4.390229e-05 4.546993e-04
## PC24 -7.967536e-04 -1.087088e-03 -5.064190e-04
## PC25 2.524151e-04 -7.599813e-05 5.808283e-04
## PC26 3.833125e-04 4.667886e-05 7.199461e-04
## PC27 2.715470e-04 -6.361989e-05 6.067139e-04
## PC29 3.679176e-04 -5.941506e-06 7.417766e-04
## PC32 -7.123956e-04 -1.128028e-03 -2.967633e-04
## PC33 7.039065e-04 2.795701e-04 1.128243e-03
## PC34 1.099756e-03 6.511037e-04 1.548408e-03
## PC37 -3.603607e-04 -8.610729e-04 1.403515e-04
## PC38 2.032648e-04 -3.141561e-04 7.206857e-04
## PC39 -2.080906e-04 -7.413170e-04 3.251358e-04
## PC42 -2.251949e-04 -7.889242e-04 3.385343e-04
## PC44 6.421781e-04 7.553640e-05 1.208820e-03
## PC45 -2.968457e-04 -8.659781e-04 2.722868e-04
## PC47 -4.846403e-04 -1.054791e-03 8.551069e-05
## PC49 3.431287e-04 -2.384184e-04 9.246758e-04
## PC57 -7.572567e-04 -1.370314e-03 -1.441993e-04
## PC59 9.818223e-04 3.716729e-04 1.591972e-03
## PC62 -3.745738e-04 -1.004500e-03 2.553524e-04
## PC63 -7.029549e-04 -1.328927e-03 -7.698276e-05
## PC64 -9.023538e-04 -1.535550e-03 -2.691578e-04
## PC66 -4.331374e-04 -1.073173e-03 2.068977e-04
## PC68 4.950411e-04 -1.474936e-04 1.137576e-03
## PC71 5.213597e-04 -1.282802e-04 1.171000e-03
## PC73 4.679612e-04 -1.857211e-04 1.121643e-03
## PC74 -6.580551e-04 -1.315861e-03 -2.495721e-07
## PC75 -8.829193e-04 -1.546441e-03 -2.193976e-04
## PC77 4.911264e-04 -1.697421e-04 1.151995e-03
## PC78 2.765648e-04 -3.878102e-04 9.409398e-04
## PC79 5.663015e-04 -1.042508e-04 1.236854e-03
## PC81 7.267212e-04 5.523200e-05 1.398210e-03
## PC82 4.337908e-04 -2.533935e-04 1.120975e-03
## PC83 -7.194573e-04 -1.403123e-03 -3.579173e-05
## PC84 7.996992e-04 1.137021e-04 1.485696e-03
## PC85 1.123558e-03 4.290312e-04 1.818084e-03
## PC87 1.719575e-03 1.029988e-03 2.409162e-03
## PC88 -1.139771e-03 -1.842020e-03 -4.375212e-04
## PC89 -5.395392e-04 -1.239624e-03 1.605451e-04
## PC90 -5.072518e-04 -1.208860e-03 1.943566e-04
## PC92 2.749095e-04 -4.208083e-04 9.706273e-04
## PC94 -9.179035e-04 -1.626069e-03 -2.097378e-04
## PC96 -4.613714e-04 -1.176317e-03 2.535744e-04
## PC97 -5.007501e-04 -1.211172e-03 2.096717e-04
## PC98 -4.817032e-04 -1.191269e-03 2.278624e-04
## PC99 -4.487862e-04 -1.159985e-03 2.624125e-04
## PC102 -5.760555e-04 -1.289414e-03 1.373025e-04
## PC104 -6.682706e-04 -1.388170e-03 5.162844e-05
## PC105 4.955110e-04 -2.268609e-04 1.217883e-03
## PC106 1.242436e-03 5.179929e-04 1.966879e-03
## PC107 6.103805e-04 -1.150509e-04 1.335812e-03
## PC109 5.375521e-04 -1.881497e-04 1.263254e-03
## PC110 -5.635217e-04 -1.293753e-03 1.667097e-04
## PC111 -8.082237e-04 -1.541821e-03 -7.462696e-05
## PC113 3.104138e-04 -4.253179e-04 1.046145e-03
## PC114 -7.563989e-04 -1.484119e-03 -2.867898e-05
## PC115 -1.655666e-03 -2.389151e-03 -9.221812e-04
## PC118 7.180344e-04 -2.119439e-05 1.457263e-03
## PC119 -5.373825e-04 -1.276933e-03 2.021678e-04
## PC121 -4.009325e-04 -1.143311e-03 3.414462e-04
## PC122 4.979362e-04 -2.400266e-04 1.235899e-03
## PC123 -5.413550e-04 -1.285929e-03 2.032187e-04
## PC125 4.774826e-04 -2.684608e-04 1.223426e-03
## PC128 -9.910001e-04 -1.736981e-03 -2.450190e-04
## PC130 4.081361e-04 -3.380762e-04 1.154348e-03
## PC131 -1.474609e-03 -2.219450e-03 -7.297668e-04
## PC132 3.074585e-04 -4.456296e-04 1.060547e-03
## PC134 9.756772e-04 2.242233e-04 1.727131e-03
## PC135 4.401274e-04 -3.112522e-04 1.191507e-03
## PC136 5.537986e-04 -2.028168e-04 1.310414e-03
## PC137 -7.524878e-04 -1.508038e-03 3.062572e-06
## PC138 5.529543e-04 -2.063313e-04 1.312240e-03
## PC139 -7.448016e-04 -1.499809e-03 1.020571e-05
## PC140 -3.901045e-04 -1.147415e-03 3.672062e-04
## PC141 3.924341e-04 -3.613440e-04 1.146212e-03
## PC143 3.158275e-04 -4.421895e-04 1.073844e-03
## PC144 1.024203e-03 2.633283e-04 1.785078e-03
## PC146 5.923295e-04 -1.751615e-04 1.359820e-03
## PC148 -5.130788e-04 -1.275746e-03 2.495885e-04
## PC151 6.756695e-04 -9.189504e-05 1.443234e-03
## PC152 -6.885784e-04 -1.455780e-03 7.862350e-05
## PC153 4.660142e-04 -3.072961e-04 1.239325e-03
## PC154 -8.514425e-04 -1.620867e-03 -8.201780e-05
## PC155 1.067769e-03 2.971624e-04 1.838375e-03
## PC156 1.368886e-03 5.966260e-04 2.141146e-03
## PC159 2.124070e-03 1.347256e-03 2.900884e-03
## PC161 3.374139e-04 -4.362380e-04 1.111066e-03
## PC162 -1.145268e-03 -1.925606e-03 -3.649295e-04
## PC163 6.712821e-04 -1.039883e-04 1.446553e-03
## PC164 3.014931e-04 -4.803026e-04 1.083289e-03Test
if (algo.stepwise.caret == TRUE){
test.model(model.stepwise, data.test
,method = 'leapSeq',subopt = NULL
,formula = formula, feature.names = feature.names, label.names = label.names
,id = id
,draw.limits = TRUE, transformation = t)
}## [1] "Summary of predicted values: "
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 2.024 2.087 2.101 2.097 2.110 2.141
## [1] "leapSeq Test MSE: 0.00102089613568135"
## [1] "leapSeq Test RMSE: 0.0319514653135244"
## [1] "leapSeq Test MSE (Org Scale): 90.4181132605642"
## [1] "leapSeq Test RMSE (Org Scale): 9.50884394974301"
LASSO with CV
Train
if (algo.LASSO.caret == TRUE){
set.seed(1)
tune.grid= expand.grid(alpha = 1,lambda = 10^seq(from=-4,to=-2,length=100))
returned = train.caret.glmselect(formula = formula
,data = data.train
,method = "glmnet"
,subopt = 'LASSO'
,tune.grid = tune.grid
,feature.names = feature.names)
model.LASSO.caret = returned$model
}## Aggregating results
## Selecting tuning parameters
## Fitting alpha = 1, lambda = 0.000242 on full training set
## glmnet
##
## 5584 samples
## 164 predictor
##
## No pre-processing
## Resampling: Cross-Validated (10 fold)
## Summary of sample sizes: 5026, 5026, 5026, 5025, 5025, 5026, ...
## Resampling results across tuning parameters:
##
## lambda RMSE Rsquared MAE
## 0.0001000000 0.03192334 0.23256979 0.02479329
## 0.0001047616 0.03192017 0.23267315 0.02479126
## 0.0001097499 0.03191703 0.23277572 0.02478938
## 0.0001149757 0.03191385 0.23288053 0.02478753
## 0.0001204504 0.03191066 0.23298596 0.02478569
## 0.0001261857 0.03190749 0.23309164 0.02478383
## 0.0001321941 0.03190440 0.23319475 0.02478200
## 0.0001384886 0.03190140 0.23329419 0.02478012
## 0.0001450829 0.03189843 0.23339333 0.02477823
## 0.0001519911 0.03189562 0.23348725 0.02477657
## 0.0001592283 0.03189296 0.23357676 0.02477519
## 0.0001668101 0.03189018 0.23367509 0.02477367
## 0.0001747528 0.03188737 0.23377816 0.02477232
## 0.0001830738 0.03188463 0.23388173 0.02477097
## 0.0001917910 0.03188206 0.23398354 0.02476972
## 0.0002009233 0.03187977 0.23407637 0.02476863
## 0.0002104904 0.03187780 0.23415956 0.02476783
## 0.0002205131 0.03187626 0.23422798 0.02476719
## 0.0002310130 0.03187533 0.23427468 0.02476696
## 0.0002420128 0.03187494 0.23430291 0.02476707
## 0.0002535364 0.03187510 0.23431317 0.02476740
## 0.0002656088 0.03187590 0.23430039 0.02476839
## 0.0002782559 0.03187739 0.23426395 0.02476974
## 0.0002915053 0.03187977 0.23419148 0.02477165
## 0.0003053856 0.03188317 0.23407928 0.02477458
## 0.0003199267 0.03188711 0.23395152 0.02477761
## 0.0003351603 0.03189166 0.23380596 0.02478130
## 0.0003511192 0.03189713 0.23362920 0.02478560
## 0.0003678380 0.03190367 0.23341163 0.02479020
## 0.0003853529 0.03191097 0.23317238 0.02479551
## 0.0004037017 0.03191924 0.23289975 0.02480145
## 0.0004229243 0.03192820 0.23261015 0.02480729
## 0.0004430621 0.03193818 0.23228786 0.02481309
## 0.0004641589 0.03194906 0.23194155 0.02481965
## 0.0004862602 0.03196120 0.23155432 0.02482729
## 0.0005094138 0.03197351 0.23118155 0.02483491
## 0.0005336699 0.03198675 0.23078424 0.02484329
## 0.0005590810 0.03200042 0.23038950 0.02485163
## 0.0005857021 0.03201532 0.22995369 0.02486049
## 0.0006135907 0.03203109 0.22950639 0.02486990
## 0.0006428073 0.03204891 0.22898306 0.02488025
## 0.0006734151 0.03206727 0.22846153 0.02489139
## 0.0007054802 0.03208805 0.22784197 0.02490477
## 0.0007390722 0.03210996 0.22719088 0.02491979
## 0.0007742637 0.03213294 0.22651181 0.02493579
## 0.0008111308 0.03215731 0.22579164 0.02495384
## 0.0008497534 0.03218442 0.22494940 0.02497414
## 0.0008902151 0.03221414 0.22400519 0.02499562
## 0.0009326033 0.03224739 0.22289891 0.02501976
## 0.0009770100 0.03228350 0.22167081 0.02504595
## 0.0010235310 0.03232380 0.22023798 0.02507435
## 0.0010722672 0.03236547 0.21876291 0.02510399
## 0.0011233240 0.03240940 0.21718667 0.02513565
## 0.0011768120 0.03245364 0.21563813 0.02516799
## 0.0012328467 0.03249995 0.21401243 0.02520142
## 0.0012915497 0.03254912 0.21227700 0.02523695
## 0.0013530478 0.03260043 0.21046509 0.02527522
## 0.0014174742 0.03265429 0.20854376 0.02531525
## 0.0014849683 0.03271106 0.20647906 0.02535810
## 0.0015556761 0.03277112 0.20425059 0.02540337
## 0.0016297508 0.03283540 0.20179158 0.02545144
## 0.0017073526 0.03290516 0.19902730 0.02550423
## 0.0017886495 0.03298082 0.19590619 0.02556229
## 0.0018738174 0.03306077 0.19251228 0.02562364
## 0.0019630407 0.03314578 0.18877667 0.02568779
## 0.0020565123 0.03322949 0.18515876 0.02575014
## 0.0021544347 0.03331246 0.18159591 0.02580962
## 0.0022570197 0.03339381 0.17819523 0.02586751
## 0.0023644894 0.03347421 0.17488529 0.02592473
## 0.0024770764 0.03355633 0.17148879 0.02598385
## 0.0025950242 0.03363977 0.16798637 0.02604424
## 0.0027185882 0.03372235 0.16459504 0.02610526
## 0.0028480359 0.03380349 0.16130186 0.02616583
## 0.0029836472 0.03388369 0.15816282 0.02622547
## 0.0031257158 0.03396480 0.15500184 0.02628510
## 0.0032745492 0.03405060 0.15153449 0.02634950
## 0.0034304693 0.03414351 0.14749356 0.02641832
## 0.0035938137 0.03424253 0.14294475 0.02649136
## 0.0037649358 0.03434815 0.13774584 0.02657044
## 0.0039442061 0.03445578 0.13227803 0.02665017
## 0.0041320124 0.03456599 0.12638303 0.02673120
## 0.0043287613 0.03467759 0.12020088 0.02681305
## 0.0045348785 0.03479095 0.11353937 0.02689610
## 0.0047508102 0.03490180 0.10689398 0.02697584
## 0.0049770236 0.03500839 0.10024208 0.02705378
## 0.0052140083 0.03509728 0.09540295 0.02711916
## 0.0054622772 0.03517456 0.09155183 0.02717667
## 0.0057223677 0.03523679 0.08951061 0.02722314
## 0.0059948425 0.03528814 0.08887341 0.02726169
## 0.0062802914 0.03533959 0.08867342 0.02729983
## 0.0065793322 0.03539414 0.08867342 0.02733970
## 0.0068926121 0.03545391 0.08867342 0.02738302
## 0.0072208090 0.03551938 0.08867342 0.02743051
## 0.0075646333 0.03559108 0.08867342 0.02748282
## 0.0079248290 0.03566959 0.08867342 0.02753976
## 0.0083021757 0.03575554 0.08867342 0.02760157
## 0.0086974900 0.03584961 0.08867342 0.02766887
## 0.0091116276 0.03595256 0.08867342 0.02774301
## 0.0095454846 0.03606519 0.08867342 0.02782424
## 0.0100000000 0.03618838 0.08867342 0.02791214
##
## Tuning parameter 'alpha' was held constant at a value of 1
## RMSE was used to select the optimal model using the smallest value.
## The final values used for the model were alpha = 1 and lambda = 0.0002420128.
## alpha lambda
## 20 1 0.0002420128
## alpha lambda RMSE Rsquared MAE RMSESD RsquaredSD MAESD
## 1 1 0.0001000000 0.03192334 0.23256979 0.02479329 0.001501843 0.04117543 0.0009669122
## 2 1 0.0001047616 0.03192017 0.23267315 0.02479126 0.001500449 0.04117915 0.0009645980
## 3 1 0.0001097499 0.03191703 0.23277572 0.02478938 0.001499021 0.04118413 0.0009623065
## 4 1 0.0001149757 0.03191385 0.23288053 0.02478753 0.001497539 0.04119032 0.0009601090
## 5 1 0.0001204504 0.03191066 0.23298596 0.02478569 0.001495986 0.04119790 0.0009578472
## 6 1 0.0001261857 0.03190749 0.23309164 0.02478383 0.001494337 0.04120347 0.0009554591
## 7 1 0.0001321941 0.03190440 0.23319475 0.02478200 0.001492604 0.04120761 0.0009529807
## 8 1 0.0001384886 0.03190140 0.23329419 0.02478012 0.001490736 0.04120703 0.0009503189
## 9 1 0.0001450829 0.03189843 0.23339333 0.02477823 0.001488791 0.04120402 0.0009474227
## 10 1 0.0001519911 0.03189562 0.23348725 0.02477657 0.001486889 0.04120382 0.0009444715
## 11 1 0.0001592283 0.03189296 0.23357676 0.02477519 0.001484980 0.04120548 0.0009416023
## 12 1 0.0001668101 0.03189018 0.23367509 0.02477367 0.001483047 0.04121763 0.0009386812
## 13 1 0.0001747528 0.03188737 0.23377816 0.02477232 0.001480936 0.04123592 0.0009356406
## 14 1 0.0001830738 0.03188463 0.23388173 0.02477097 0.001478798 0.04126336 0.0009325507
## 15 1 0.0001917910 0.03188206 0.23398354 0.02476972 0.001476714 0.04129762 0.0009295913
## 16 1 0.0002009233 0.03187977 0.23407637 0.02476863 0.001474469 0.04132824 0.0009266080
## 17 1 0.0002104904 0.03187780 0.23415956 0.02476783 0.001472225 0.04136367 0.0009234413
## 18 1 0.0002205131 0.03187626 0.23422798 0.02476719 0.001469878 0.04140120 0.0009200294
## 19 1 0.0002310130 0.03187533 0.23427468 0.02476696 0.001467392 0.04144430 0.0009165122
## 20 1 0.0002420128 0.03187494 0.23430291 0.02476707 0.001464642 0.04147838 0.0009125592
## 21 1 0.0002535364 0.03187510 0.23431317 0.02476740 0.001461773 0.04151042 0.0009083437
## 22 1 0.0002656088 0.03187590 0.23430039 0.02476839 0.001458755 0.04153785 0.0009037501
## 23 1 0.0002782559 0.03187739 0.23426395 0.02476974 0.001455688 0.04156229 0.0008990177
## 24 1 0.0002915053 0.03187977 0.23419148 0.02477165 0.001452326 0.04156849 0.0008937243
## 25 1 0.0003053856 0.03188317 0.23407928 0.02477458 0.001448839 0.04157442 0.0008884160
## 26 1 0.0003199267 0.03188711 0.23395152 0.02477761 0.001445094 0.04157744 0.0008828587
## 27 1 0.0003351603 0.03189166 0.23380596 0.02478130 0.001441000 0.04157508 0.0008768307
## 28 1 0.0003511192 0.03189713 0.23362920 0.02478560 0.001436661 0.04156644 0.0008702125
## 29 1 0.0003678380 0.03190367 0.23341163 0.02479020 0.001431963 0.04154425 0.0008628696
## 30 1 0.0003853529 0.03191097 0.23317238 0.02479551 0.001427161 0.04151684 0.0008551571
## 31 1 0.0004037017 0.03191924 0.23289975 0.02480145 0.001422319 0.04147053 0.0008474630
## 32 1 0.0004229243 0.03192820 0.23261015 0.02480729 0.001417270 0.04141539 0.0008397799
## 33 1 0.0004430621 0.03193818 0.23228786 0.02481309 0.001412321 0.04135100 0.0008320904
## 34 1 0.0004641589 0.03194906 0.23194155 0.02481965 0.001407210 0.04129646 0.0008247388
## 35 1 0.0004862602 0.03196120 0.23155432 0.02482729 0.001401684 0.04122082 0.0008168112
## 36 1 0.0005094138 0.03197351 0.23118155 0.02483491 0.001396227 0.04115218 0.0008088982
## 37 1 0.0005336699 0.03198675 0.23078424 0.02484329 0.001390415 0.04105535 0.0008009227
## 38 1 0.0005590810 0.03200042 0.23038950 0.02485163 0.001384973 0.04097258 0.0007936120
## 39 1 0.0005857021 0.03201532 0.22995369 0.02486049 0.001379106 0.04083810 0.0007862218
## 40 1 0.0006135907 0.03203109 0.22950639 0.02486990 0.001373708 0.04071931 0.0007792893
## 41 1 0.0006428073 0.03204891 0.22898306 0.02488025 0.001368244 0.04057154 0.0007726106
## 42 1 0.0006734151 0.03206727 0.22846153 0.02489139 0.001364492 0.04051577 0.0007678790
## 43 1 0.0007054802 0.03208805 0.22784197 0.02490477 0.001361221 0.04049606 0.0007639254
## 44 1 0.0007390722 0.03210996 0.22719088 0.02491979 0.001357544 0.04044563 0.0007599225
## 45 1 0.0007742637 0.03213294 0.22651181 0.02493579 0.001352999 0.04031782 0.0007549115
## 46 1 0.0008111308 0.03215731 0.22579164 0.02495384 0.001348941 0.04018886 0.0007492863
## 47 1 0.0008497534 0.03218442 0.22494940 0.02497414 0.001344495 0.04002042 0.0007436798
## 48 1 0.0008902151 0.03221414 0.22400519 0.02499562 0.001340150 0.03986803 0.0007403559
## 49 1 0.0009326033 0.03224739 0.22289891 0.02501976 0.001336185 0.03973059 0.0007379907
## 50 1 0.0009770100 0.03228350 0.22167081 0.02504595 0.001332016 0.03957195 0.0007349972
## 51 1 0.0010235310 0.03232380 0.22023798 0.02507435 0.001327697 0.03938553 0.0007319502
## 52 1 0.0010722672 0.03236547 0.21876291 0.02510399 0.001323829 0.03925974 0.0007292941
## 53 1 0.0011233240 0.03240940 0.21718667 0.02513565 0.001319038 0.03910563 0.0007270796
## 54 1 0.0011768120 0.03245364 0.21563813 0.02516799 0.001316957 0.03915390 0.0007274704
## 55 1 0.0012328467 0.03249995 0.21401243 0.02520142 0.001315040 0.03921183 0.0007276348
## 56 1 0.0012915497 0.03254912 0.21227700 0.02523695 0.001313745 0.03934112 0.0007276793
## 57 1 0.0013530478 0.03260043 0.21046509 0.02527522 0.001312148 0.03941792 0.0007281206
## 58 1 0.0014174742 0.03265429 0.20854376 0.02531525 0.001311329 0.03951368 0.0007287620
## 59 1 0.0014849683 0.03271106 0.20647906 0.02535810 0.001311430 0.03954985 0.0007298514
## 60 1 0.0015556761 0.03277112 0.20425059 0.02540337 0.001312794 0.03964692 0.0007317700
## 61 1 0.0016297508 0.03283540 0.20179158 0.02545144 0.001314320 0.03972683 0.0007338245
## 62 1 0.0017073526 0.03290516 0.19902730 0.02550423 0.001316736 0.03989129 0.0007357228
## 63 1 0.0017886495 0.03298082 0.19590619 0.02556229 0.001318781 0.04003413 0.0007377281
## 64 1 0.0018738174 0.03306077 0.19251228 0.02562364 0.001319783 0.04010579 0.0007392430
## 65 1 0.0019630407 0.03314578 0.18877667 0.02568779 0.001320381 0.04004958 0.0007405088
## 66 1 0.0020565123 0.03322949 0.18515876 0.02575014 0.001321319 0.04016913 0.0007421136
## 67 1 0.0021544347 0.03331246 0.18159591 0.02580962 0.001319478 0.04002657 0.0007408500
## 68 1 0.0022570197 0.03339381 0.17819523 0.02586751 0.001320650 0.04017659 0.0007402892
## 69 1 0.0023644894 0.03347421 0.17488529 0.02592473 0.001320061 0.04003338 0.0007376674
## 70 1 0.0024770764 0.03355633 0.17148879 0.02598385 0.001319651 0.03999356 0.0007356338
## 71 1 0.0025950242 0.03363977 0.16798637 0.02604424 0.001313531 0.03959595 0.0007289423
## 72 1 0.0027185882 0.03372235 0.16459504 0.02610526 0.001307551 0.03943793 0.0007235330
## 73 1 0.0028480359 0.03380349 0.16130186 0.02616583 0.001296572 0.03880615 0.0007145113
## 74 1 0.0029836472 0.03388369 0.15816282 0.02622547 0.001285548 0.03830745 0.0007058147
## 75 1 0.0031257158 0.03396480 0.15500184 0.02628510 0.001273499 0.03752033 0.0006953765
## 76 1 0.0032745492 0.03405060 0.15153449 0.02634950 0.001262952 0.03679102 0.0006850448
## 77 1 0.0034304693 0.03414351 0.14749356 0.02641832 0.001252239 0.03596074 0.0006748276
## 78 1 0.0035938137 0.03424253 0.14294475 0.02649136 0.001244117 0.03535746 0.0006675857
## 79 1 0.0037649358 0.03434815 0.13774584 0.02657044 0.001238157 0.03459906 0.0006609773
## 80 1 0.0039442061 0.03445578 0.13227803 0.02665017 0.001231678 0.03404481 0.0006551871
## 81 1 0.0041320124 0.03456599 0.12638303 0.02673120 0.001221807 0.03304916 0.0006477175
## 82 1 0.0043287613 0.03467759 0.12020088 0.02681305 0.001211126 0.03227306 0.0006412668
## 83 1 0.0045348785 0.03479095 0.11353937 0.02689610 0.001194181 0.03085990 0.0006302547
## 84 1 0.0047508102 0.03490180 0.10689398 0.02697584 0.001178457 0.02996663 0.0006212900
## 85 1 0.0049770236 0.03500839 0.10024208 0.02705378 0.001160715 0.02791788 0.0006073701
## 86 1 0.0052140083 0.03509728 0.09540295 0.02711916 0.001152257 0.02769593 0.0006021656
## 87 1 0.0054622772 0.03517456 0.09155183 0.02717667 0.001140811 0.02658807 0.0005930574
## 88 1 0.0057223677 0.03523679 0.08951061 0.02722314 0.001138263 0.02713387 0.0005900847
## 89 1 0.0059948425 0.03528814 0.08887341 0.02726169 0.001135241 0.02690684 0.0005846312
## 90 1 0.0062802914 0.03533959 0.08867342 0.02729983 0.001133208 0.02694524 0.0005791697
## 91 1 0.0065793322 0.03539414 0.08867342 0.02733970 0.001129139 0.02694524 0.0005723130
## 92 1 0.0068926121 0.03545391 0.08867342 0.02738302 0.001125048 0.02694524 0.0005662155
## 93 1 0.0072208090 0.03551938 0.08867342 0.02743051 0.001120960 0.02694524 0.0005601812
## 94 1 0.0075646333 0.03559108 0.08867342 0.02748282 0.001116907 0.02694524 0.0005542403
## 95 1 0.0079248290 0.03566959 0.08867342 0.02753976 0.001112924 0.02694524 0.0005479786
## 96 1 0.0083021757 0.03575554 0.08867342 0.02760157 0.001109056 0.02694524 0.0005425216
## 97 1 0.0086974900 0.03584961 0.08867342 0.02766887 0.001105354 0.02694524 0.0005380517
## 98 1 0.0091116276 0.03595256 0.08867342 0.02774301 0.001101878 0.02694524 0.0005338495
## 99 1 0.0095454846 0.03606519 0.08867342 0.02782424 0.001098697 0.02694524 0.0005304576
## 100 1 0.0100000000 0.03618838 0.08867342 0.02791214 0.001095894 0.02694524 0.0005287606
## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
## [1] "Coefficients"
## model.coef
## (Intercept) 2.096897e+00
## PC1 -4.645913e-04
## PC2 -9.239349e-04
## PC3 -4.166302e-04
## PC4 -3.268518e-04
## PC5 2.077041e-04
## PC6 -7.707639e-05
## PC7 -1.779289e-04
## PC8 -1.557523e-05
## PC9 -2.837554e-05
## PC11 -5.131010e-04
## PC12 -4.759358e-04
## PC13 3.137947e-04
## PC14 2.261062e-04
## PC15 -6.529096e-06
## PC16 3.269539e-04
## PC17 -1.683571e-04
## PC18 -3.317640e-04
## PC19 8.307391e-06
## PC20 3.715853e-04
## PC21 3.692625e-05
## PC22 3.022817e-05
## PC23 1.313795e-04
## PC24 -7.069816e-04
## PC25 1.570665e-04
## PC26 2.893206e-04
## PC27 1.710490e-04
## PC29 2.576447e-04
## PC32 -5.914603e-04
## PC33 5.727051e-04
## PC34 9.771484e-04
## PC37 -2.149451e-04
## PC38 5.590158e-05
## PC39 -4.145978e-05
## PC42 -4.539262e-05
## PC44 4.711501e-04
## PC45 -1.257630e-04
## PC47 -3.273804e-04
## PC49 1.703726e-04
## PC57 -5.540830e-04
## PC59 8.058432e-04
## PC62 -1.869748e-04
## PC63 -5.226898e-04
## PC64 -7.204755e-04
## PC66 -2.269471e-04
## PC67 2.998784e-05
## PC68 3.191289e-04
## PC70 3.142512e-06
## PC71 3.370170e-04
## PC73 2.724797e-04
## PC74 -4.572800e-04
## PC75 -6.720971e-04
## PC77 2.936744e-04
## PC78 8.005685e-05
## PC79 3.747930e-04
## PC81 5.257753e-04
## PC82 2.264838e-04
## PC83 -5.218655e-04
## PC84 5.929189e-04
## PC85 9.285516e-04
## PC87 1.512129e-03
## PC88 -9.333071e-04
## PC89 -3.345004e-04
## PC90 -2.833801e-04
## PC92 4.182425e-05
## PC94 -7.278763e-04
## PC96 -2.507284e-04
## PC97 -3.099825e-04
## PC98 -2.447097e-04
## PC99 -2.276525e-04
## PC102 -3.742401e-04
## PC104 -4.572499e-04
## PC105 3.051800e-04
## PC106 1.034008e-03
## PC107 4.147117e-04
## PC109 3.091838e-04
## PC110 -3.572508e-04
## PC111 -5.961771e-04
## PC113 1.188012e-04
## PC114 -5.445481e-04
## PC115 -1.437879e-03
## PC118 4.873668e-04
## PC119 -3.017491e-04
## PC120 1.052595e-05
## PC121 -2.001836e-04
## PC122 2.978399e-04
## PC123 -3.427091e-04
## PC124 3.724332e-06
## PC125 2.597312e-04
## PC128 -7.720717e-04
## PC130 1.941239e-04
## PC131 -1.260735e-03
## PC132 8.517374e-05
## PC134 7.867958e-04
## PC135 2.208958e-04
## PC136 3.151148e-04
## PC137 -5.333841e-04
## PC138 3.446180e-04
## PC139 -5.188744e-04
## PC140 -1.482569e-04
## PC141 1.830576e-04
## PC143 9.390756e-05
## PC144 8.248566e-04
## PC146 3.533680e-04
## PC147 -5.275278e-05
## PC148 -2.979852e-04
## PC151 4.423910e-04
## PC152 -4.479116e-04
## PC153 2.465481e-04
## PC154 -6.137170e-04
## PC155 8.525282e-04
## PC156 1.145196e-03
## PC157 -2.047709e-05
## PC159 1.882328e-03
## PC160 1.484216e-06
## PC161 9.546170e-05
## PC162 -9.153109e-04
## PC163 4.515326e-04
## PC164 8.160572e-05Test
if (algo.LASSO.caret == TRUE){
test.model(model.LASSO.caret, data.test
,method = 'glmnet',subopt = "LASSO"
,formula = formula, feature.names = feature.names, label.names = label.names
,draw.limits = TRUE, transformation = t)
}## [1] "Summary of predicted values: "
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 2.030 2.088 2.101 2.097 2.109 2.138
## [1] "glmnet LASSO Test MSE: 0.00100661928020248"
## [1] "glmnet LASSO Test RMSE: 0.0317272639886026"
## [1] "glmnet LASSO Test MSE (Org Scale): 89.2044921717936"
## [1] "glmnet LASSO Test RMSE (Org Scale): 9.44481297706808"
LARS with CV
Train
if (algo.LARS.caret == TRUE){
set.seed(1)
returned = train.caret.glmselect(formula = formula
,data = data.train
,method = "lars"
,subopt = 'NULL'
,feature.names = feature.names)
model.LARS.caret = returned$model
}## Warning in nominalTrainWorkflow(x = x, y = y, wts = weights, info = trainInfo, : There were missing values in resampled
## performance measures.## Aggregating results
## Selecting tuning parameters
## Fitting fraction = 0.758 on full training set
## Least Angle Regression
##
## 5584 samples
## 164 predictor
##
## Pre-processing: centered (164), scaled (164)
## Resampling: Cross-Validated (10 fold)
## Summary of sample sizes: 5026, 5026, 5026, 5025, 5025, 5026, ...
## Resampling results across tuning parameters:
##
## fraction RMSE Rsquared MAE
## 0.00000000 0.03638401 NaN 0.02805055
## 0.01010101 0.03599441 0.08867342 0.02777237
## 0.02020202 0.03565622 0.08867342 0.02752900
## 0.03030303 0.03537093 0.08867342 0.02732146
## 0.04040404 0.03514541 0.09297130 0.02715425
## 0.05050505 0.03494804 0.10406469 0.02700817
## 0.06060606 0.03476279 0.11546665 0.02687491
## 0.07070707 0.03459185 0.12520383 0.02674904
## 0.08080808 0.03442977 0.13387449 0.02663084
## 0.09090909 0.03427761 0.14151172 0.02651809
## 0.10101010 0.03413141 0.14839447 0.02641044
## 0.11111111 0.03399660 0.15405935 0.02631023
## 0.12121212 0.03387507 0.15865918 0.02621943
## 0.13131313 0.03376483 0.16295499 0.02613672
## 0.14141414 0.03366009 0.16721288 0.02605904
## 0.15151515 0.03355785 0.17150886 0.02598414
## 0.16161616 0.03346270 0.17547342 0.02591396
## 0.17171717 0.03337368 0.17916176 0.02585107
## 0.18181818 0.03328970 0.18267834 0.02579186
## 0.19191919 0.03320907 0.18619829 0.02573314
## 0.20202020 0.03313013 0.18962101 0.02567406
## 0.21212121 0.03305208 0.19299024 0.02561501
## 0.22222222 0.03297544 0.19626565 0.02555641
## 0.23232323 0.03290222 0.19930212 0.02549939
## 0.24242424 0.03283328 0.20205124 0.02544630
## 0.25252525 0.03277086 0.20443367 0.02539946
## 0.26262626 0.03271318 0.20656562 0.02535604
## 0.27272727 0.03266006 0.20845257 0.02531574
## 0.28282828 0.03261007 0.21021161 0.02527831
## 0.29292929 0.03256239 0.21190845 0.02524338
## 0.30303030 0.03251829 0.21347808 0.02521220
## 0.31313131 0.03247705 0.21493031 0.02518283
## 0.32323232 0.03243863 0.21626444 0.02515525
## 0.33333333 0.03240160 0.21756069 0.02512875
## 0.34343434 0.03236462 0.21888524 0.02510257
## 0.35353535 0.03232935 0.22014500 0.02507788
## 0.36363636 0.03229681 0.22129592 0.02505457
## 0.37373737 0.03226738 0.22229827 0.02503354
## 0.38383838 0.03223978 0.22322845 0.02501411
## 0.39393939 0.03221455 0.22405349 0.02499624
## 0.40404040 0.03219165 0.22477187 0.02497981
## 0.41414141 0.03217118 0.22537874 0.02496411
## 0.42424242 0.03215213 0.22594448 0.02494976
## 0.43434343 0.03213380 0.22649635 0.02493598
## 0.44444444 0.03211653 0.22701123 0.02492359
## 0.45454545 0.03210009 0.22749697 0.02491224
## 0.46464646 0.03208479 0.22793875 0.02490233
## 0.47474747 0.03207042 0.22835279 0.02489332
## 0.48484848 0.03205664 0.22875252 0.02488502
## 0.49494949 0.03204343 0.22913837 0.02487689
## 0.50505051 0.03203130 0.22948352 0.02486994
## 0.51515152 0.03202021 0.22979125 0.02486339
## 0.52525253 0.03200948 0.23009838 0.02485709
## 0.53535354 0.03199915 0.23039871 0.02485101
## 0.54545455 0.03198926 0.23068442 0.02484489
## 0.55555556 0.03198006 0.23094622 0.02483930
## 0.56565657 0.03197082 0.23122441 0.02483349
## 0.57575758 0.03196201 0.23149356 0.02482789
## 0.58585859 0.03195312 0.23177542 0.02482226
## 0.59595960 0.03194427 0.23206588 0.02481678
## 0.60606061 0.03193626 0.23232471 0.02481211
## 0.61616162 0.03192900 0.23255713 0.02480790
## 0.62626263 0.03192181 0.23279316 0.02480331
## 0.63636364 0.03191541 0.23299719 0.02479860
## 0.64646465 0.03190908 0.23320828 0.02479390
## 0.65656566 0.03190300 0.23341524 0.02478945
## 0.66666667 0.03189757 0.23359626 0.02478572
## 0.67676768 0.03189295 0.23374443 0.02478226
## 0.68686869 0.03188875 0.23388056 0.02477893
## 0.69696970 0.03188506 0.23399838 0.02477603
## 0.70707071 0.03188144 0.23412094 0.02477318
## 0.71717172 0.03187849 0.23421803 0.02477059
## 0.72727273 0.03187639 0.23428072 0.02476888
## 0.73737374 0.03187522 0.23430512 0.02476767
## 0.74747475 0.03187464 0.23430744 0.02476691
## 0.75757576 0.03187450 0.23429679 0.02476652
## 0.76767677 0.03187512 0.23425840 0.02476657
## 0.77777778 0.03187640 0.23419784 0.02476694
## 0.78787879 0.03187835 0.23411270 0.02476774
## 0.79797980 0.03188107 0.23399998 0.02476902
## 0.80808081 0.03188434 0.23386961 0.02477058
## 0.81818182 0.03188793 0.23373481 0.02477223
## 0.82828283 0.03189169 0.23360230 0.02477411
## 0.83838384 0.03189547 0.23347609 0.02477611
## 0.84848485 0.03189992 0.23332723 0.02477885
## 0.85858586 0.03190488 0.23316267 0.02478194
## 0.86868687 0.03191047 0.23297549 0.02478526
## 0.87878788 0.03191643 0.23278076 0.02478872
## 0.88888889 0.03192286 0.23257249 0.02479272
## 0.89898990 0.03192992 0.23234283 0.02479771
## 0.90909091 0.03193743 0.23210172 0.02480310
## 0.91919192 0.03194520 0.23185698 0.02480856
## 0.92929293 0.03195351 0.23159502 0.02481454
## 0.93939394 0.03196231 0.23131923 0.02482079
## 0.94949495 0.03197149 0.23103381 0.02482740
## 0.95959596 0.03198106 0.23073919 0.02483434
## 0.96969697 0.03199101 0.23043572 0.02484165
## 0.97979798 0.03200124 0.23012631 0.02484921
## 0.98989899 0.03201172 0.22981410 0.02485714
## 1.00000000 0.03202267 0.22948948 0.02486541
##
## RMSE was used to select the optimal model using the smallest value.
## The final value used for the model was fraction = 0.7575758.
## fraction
## 76 0.7575758## Warning: Removed 1 rows containing missing values (geom_point).
## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
## [1] "Coefficients"
## PC1 PC2 PC3 PC4 PC5 PC6 PC7 PC8
## -5.332863e-03 -1.044467e-02 -4.680589e-03 -3.622502e-03 2.236084e-03 -8.291252e-04 -1.874068e-03 -1.605598e-04
## PC9 PC11 PC12 PC13 PC14 PC15 PC16 PC17
## -2.855532e-04 -4.756169e-03 -4.184516e-03 2.708394e-03 1.885853e-03 -5.380449e-05 2.644630e-03 -1.290766e-03
## PC18 PC19 PC20 PC21 PC22 PC23 PC24 PC25
## -2.446991e-03 6.079200e-05 2.475448e-03 2.361609e-04 1.237944e-04 4.353439e-04 -2.010283e-03 3.950894e-04
## PC26 PC27 PC29 PC32 PC33 PC34 PC37 PC38
## 7.094747e-04 4.215485e-04 5.688791e-04 -1.175400e-03 1.114235e-03 1.798928e-03 -3.544679e-04 8.944137e-05
## PC39 PC42 PC44 PC45 PC47 PC49 PC57 PC59
## -6.454831e-05 -6.676989e-05 6.869316e-04 -1.826807e-04 -4.743275e-04 2.422599e-04 -7.460410e-04 1.090068e-03
## PC62 PC63 PC64 PC66 PC67 PC68 PC71 PC73
## -2.454007e-04 -6.895132e-04 -9.401858e-04 -2.930151e-04 3.909376e-05 4.104030e-04 4.284219e-04 3.446257e-04
## PC74 PC75 PC77 PC78 PC79 PC81 PC82 PC83
## -5.741967e-04 -8.363334e-04 3.672726e-04 9.976832e-05 4.620840e-04 6.463820e-04 2.722015e-04 -6.306186e-04
## PC84 PC85 PC87 PC88 PC89 PC90 PC92 PC94
## 7.135643e-04 1.104334e-03 1.809177e-03 -1.097415e-03 -3.947437e-04 -3.337717e-04 5.000256e-05 -8.486372e-04
## PC96 PC97 PC98 PC99 PC102 PC104 PC105 PC106
## -2.897960e-04 -3.601266e-04 -2.849368e-04 -2.644878e-04 -4.330857e-04 -5.243773e-04 3.487174e-04 1.178085e-03
## PC107 PC109 PC110 PC111 PC113 PC114 PC115 PC118
## 4.720819e-04 3.520929e-04 -4.040320e-04 -6.709045e-04 1.334930e-04 -6.176265e-04 -1.618772e-03 5.442466e-04
## PC119 PC120 PC121 PC122 PC123 PC124 PC125 PC128
## -3.370672e-04 1.009976e-05 -2.228765e-04 3.332371e-04 -3.799905e-04 4.799659e-07 2.876962e-04 -8.542056e-04
## PC130 PC131 PC132 PC134 PC135 PC136 PC137 PC138
## 2.150313e-04 -1.396784e-03 9.368906e-05 8.642841e-04 2.428342e-04 3.439469e-04 -5.825714e-04 3.750598e-04
## PC139 PC140 PC141 PC143 PC144 PC146 PC147 PC148
## -5.669017e-04 -1.617705e-04 2.006277e-04 1.025875e-04 8.947662e-04 3.803750e-04 -5.735677e-05 -3.227396e-04
## PC151 PC152 PC153 PC154 PC155 PC156 PC157 PC159
## 4.756667e-04 -4.821061e-04 2.634063e-04 -6.582177e-04 9.130771e-04 1.223453e-03 -2.232113e-05 1.998806e-03
## PC161 PC162 PC163 PC164
## 1.021751e-04 -9.677465e-04 4.808124e-04 8.640920e-05Test
if (algo.LARS.caret == TRUE){
test.model(model.LARS.caret, data.test
,method = 'lars',subopt = NULL
,formula = formula, feature.names = feature.names, label.names = label.names
,draw.limits = TRUE, transformation = t)
}## [1] "Summary of predicted values: "
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 2.030 2.088 2.101 2.097 2.109 2.138
## [1] "lars Test MSE: 0.00100662736899733"
## [1] "lars Test RMSE: 0.031727391462226"
## [1] "lars Test MSE (Org Scale): 89.2050390186953"
## [1] "lars Test RMSE (Org Scale): 9.44484192661239"
Session Info
sessionInfo()## R version 3.5.1 (2018-07-02)
## Platform: x86_64-w64-mingw32/x64 (64-bit)
## Running under: Windows 10 x64 (build 17134)
##
## Matrix products: default
##
## locale:
## [1] LC_COLLATE=English_United States.1252 LC_CTYPE=English_United States.1252 LC_MONETARY=English_United States.1252
## [4] LC_NUMERIC=C LC_TIME=English_United States.1252
##
## attached base packages:
## [1] parallel stats graphics grDevices utils datasets methods base
##
## other attached packages:
## [1] bindrcpp_0.2.2 knitr_1.20 htmltools_0.3.6 reshape2_1.4.3
## [5] lars_1.2 doParallel_1.0.14 iterators_1.0.10 caret_6.0-81
## [9] leaps_3.0 ggforce_0.1.3 rlist_0.4.6.1 car_3.0-2
## [13] carData_3.0-2 bestNormalize_1.3.0 scales_1.0.0 onewaytests_2.0
## [17] caTools_1.17.1.1 mosaic_1.5.0 mosaicData_0.17.0 ggformula_0.9.1
## [21] ggstance_0.3.1 lattice_0.20-35 DT_0.5 ggiraph_0.6.0
## [25] investr_1.4.0 glmnet_2.0-16 foreach_1.4.4 Matrix_1.2-14
## [29] MASS_7.3-50 PerformanceAnalytics_1.5.2 xts_0.11-2 zoo_1.8-4
## [33] forcats_0.3.0 stringr_1.3.1 dplyr_0.7.8 purrr_0.2.5
## [37] readr_1.3.1 tidyr_0.8.2 tibble_1.4.2 ggplot2_3.1.0
## [41] tidyverse_1.2.1 usdm_1.1-18 raster_2.8-4 sp_1.3-1
## [45] pacman_0.5.0
##
## loaded via a namespace (and not attached):
## [1] readxl_1.2.0 backports_1.1.3 plyr_1.8.4 lazyeval_0.2.1 splines_3.5.1 mycor_0.1.1
## [7] crosstalk_1.0.0 leaflet_2.0.2 digest_0.6.18 magrittr_1.5 mosaicCore_0.6.0 openxlsx_4.1.0
## [13] recipes_0.1.4 modelr_0.1.2 gower_0.1.2 colorspace_1.3-2 rvest_0.3.2 ggrepel_0.8.0
## [19] haven_2.0.0 crayon_1.3.4 jsonlite_1.5 bindr_0.1.1 survival_2.42-3 glue_1.3.0
## [25] registry_0.5 gtable_0.2.0 ppcor_1.1 ipred_0.9-8 abind_1.4-5 rngtools_1.3.1
## [31] bibtex_0.4.2 Rcpp_1.0.0 xtable_1.8-3 units_0.6-2 foreign_0.8-70 stats4_3.5.1
## [37] lava_1.6.4 prodlim_2018.04.18 htmlwidgets_1.3 httr_1.4.0 RColorBrewer_1.1-2 pkgconfig_2.0.2
## [43] farver_1.1.0 nnet_7.3-12 labeling_0.3 tidyselect_0.2.5 rlang_0.3.1 later_0.7.5
## [49] munsell_0.5.0 cellranger_1.1.0 tools_3.5.1 cli_1.0.1 generics_0.0.2 moments_0.14
## [55] sjlabelled_1.0.17 broom_0.5.1 evaluate_0.12 ggdendro_0.1-20 yaml_2.2.0 ModelMetrics_1.2.2
## [61] zip_2.0.1 nlme_3.1-137 doRNG_1.7.1 mime_0.6 xml2_1.2.0 compiler_3.5.1
## [67] rstudioapi_0.8 curl_3.2 tweenr_1.0.1 stringi_1.2.4 gdtools_0.1.7 pillar_1.3.1
## [73] data.table_1.11.8 bitops_1.0-6 insight_0.1.2 httpuv_1.4.5 R6_2.3.0 promises_1.0.1
## [79] gridExtra_2.3 rio_0.5.16 codetools_0.2-15 assertthat_0.2.0 pkgmaker_0.27 withr_2.1.2
## [85] nortest_1.0-4 mgcv_1.8-24 hms_0.4.2 quadprog_1.5-5 grid_3.5.1 rpart_4.1-13
## [91] timeDate_3043.102 class_7.3-14 rmarkdown_1.11 shiny_1.2.0 lubridate_1.7.4